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IS" 


2: 


THE  DETERMINATION 


OF 


HYDROGEN   IONS 

An  elementary  treatise  on  the  hydrogen  electrode,  indi- 
cator and  supplementary  methods  with  an  indexed 
bibliography  on  applications 


BY 

W.  MANSFIELD  CLARK,  M.A.,  Ph.D. 

Formerly  Chemist,  Research  Laboratories  of  the  Dairy  Division, 

United  Stales  Department  of  Agriculture, 

Professor  of  Chemistry,  Hygienic  Laboratory, 

United  States  Public  Health  Service 


SECOND  EDITION 


%  l%o  $ 


I  O    q    1<4. 


BALTIMORE 

WILLIAMS  &  WILKINS  COMPANY 

1923 


QD 
50,  \ 


First  Edition,  September,  1920 

Reprinted,  May,  1921 

Second  Edition,  September,  1922 

Reprinted,  May,  1928 


Copyright  1922 
Williams  &  Wilkins  Company 

All  rights  reserved,  including  that  of  translation  into  foreign  languages, 
including  the  Scandinavian 


To 

Fellow  Workers  in  the  Biological  Sciences, 

Architects  of  Progress, 

Who  Hew  the  Stone  to  Build  Where  Unseen  Spires  Shall  Stand 


TABLE  OF  CONTENTS 

I.  Introduction.    Some   General  Relations   Among  Acids 

and  Bases 15 

The  nature  of  electrolytic  dissociation 15 

Reversible  reactions  and  chemical  equilibria 16 

The  equilibrium  equation  for  acid  dissociation 18 

The  equilibrium  equation  for  base  dissociation 20 

The  water  equilibrium 21 

Titration  curves 22 

Percentage  dissociation  curves 24 

Amphoters 30 

II.  Some  Special  Aspects  of  Acid-base  Equilibria 34 

"  The  pH  scale 34 

/  The  effect  of  dilution 37 

-     Buffer  action 39 

The  conduct  of  strong  electrolytes 44 

v/III.  Outline  of  a  Colorimetric  Method 48 

Color  chart.    Water  color  by  Broedel,  color  press  work 

by  F.  Goeb between  50  and    51 

IV.  Theory  of  Indicators 54 

Outline  of  the  Ostwald  theory 55 

Tautomerism 59 

Optical  aspects 62 

V.  Choice  of  Indicators 73 

Review  of  available  material 74 

S0rensen's  selection 78 

Clark  and  Lubs'  selection 80 

Michaelis'  selection 82 

Tables  of  indicators  with  their  pH  ranges 84-94 

Indicator  synonyms 95 

VI.  Standard  Buffer  Solutions  for  Colorimetric  Comparison    99 
Preparation  of  materials  for  Clark  and  Lubs'  solutions.     100 

Clark  and  Lubs'  buffer  solutions 106 

Preparation  of  materials  for  S0rensen's  solutions 107 

S0rensen's  solutions 111-114 

Other  solutions 115 

VII.  Sources  of  Error  in  Colorimetric  Determinations 118 

Salt  errors 118 

Protein  errors 122 

Other  errors 123 

Effect  of  temperature  variation 123 

VIII.  Approximate  Determinations  with  Indicators 126 

Judgment  by  unaided  eye 126 

Gillespie's  method 127 

5 


6  CONTENTS 

Michaelis'  method 132 

Indicator  paper 138 

Dilution 139 

Use  of  indicators  in  bacteriology 140 

Special  uses 142 

Spotting ' 143 

IX.  Outline  of  the  Electrometric  Method 144 

X.  Theory  of  the  Hydrogen  Electrode 151 

Potential  differences  between  electrodes  and  solutions. . . .  151 
Derivation  of  equation  relating  electrode  potential  dif- 
ference to  concentration 152 

Equation  for  concentration  chain 154 

Derivation  of  numerical  form  of  equation 155 

The  "normal  hydrogen  electrode." 157 

Barometric  correction 159 

Final  working  equation 161 

XI.  Potential  Differences  at  Liquid  Junctions 163 

The  cause 163 

Equations   used   in   the   calculation   of   liquid   junction 

potential  differences 164 

Experimental  studies 167 

The  employment  of  saturated  KC1  solutions 168 

Summary  of  general  conclusions 171 

XII.  Hydrogen  Electrodes  and  Electrode  Vessels 173 

Construction  of  electrodes 173 

Deposition  of  "black." 175 

Hydrogen  electrode  vessels 178 

XIII.  Calomel  Electrodes 191 

The  general  principles  and  structure 191 

Chemical  preparation  of  calomel 191 

Electro-chemical  preparation  of  calomel 192 

Variations  of  potential 192 

Calomel  electrode  vessels 194 

Values  assigned  to  potential  differences 195 

XIV.  The  Potentiometer  and  Accessory  Equipment 201 

The  principle  of  the  potentiometer 201 

A  simple  potentiometer 202 

The  Leeds  and  Northrup  instrument 203 

A  resistance  box  system 205 

Volt-meter,  system 207 

Ballistic  galvanometer  method  of  measurement 208 

Use  of  the  electron  tube 210 

Null  point  instruments 212 

The  galvanometer 212 

The  capillary  electrometer 213 

The  quadrant  electrometer 214 

The  telephone  receiver 216 


CONTENTS  7 

Selection  of  null  point  instrument  characteristics 216 

Potentiometer  characteristics 219 

The  Weston  standard  cell 221 

Storage  batteries 224 

XV.  Hydrogen  Generators,  Wiring,  Shielding,  Temperature 

Control,  Purification  of  Mercury 227 

XVI.  The  Relation  of  Hydrogen  Electrode  Potentials  to 

Reduction  Potentials 242 

Relations  based  on  assumption  that  reductant  reacts  with 

hydrogen  ion  or  with  water 243 

Difficulties  encountered 245 

The  postulate  of  electron  concentration 247 

Electrode  equation  involving  electron  concentration 251 

Coordination  of  electrode  equations 251 

Discussion  based  on  the  coordination 253 

Some  elementary  relations  of  hydrogen  ion  concentrations 

to  observed  "reduction  potentials." 256 

XVII.  Sources  of  Error  in  Electrometric  Measurements  of  pH.  264 
XVIII.  Standard  Solutions  for  Checking  Hydrogen  Electrode 

Measurements 271 

XIX.  The  Standardization  of  pH  Measurements 276 

Absence  of  a  precise  basis 277  ~ * 

Values  used  for  standard  electrodes 280  ct    ft&tCfi 

Necessity  for  standardization 286 

Proposal  of  standard  values 287 

i  Experimental  definition  of  pH 287*5 Ml  Uit      * 

XX.  Supplementary  Methods 289  cf  fM  f# 

The  quinhydrone  electrode 289 \'^/icc0uOUf 

Conductivity 293    fy  /tfxsyfM 

Catalytic  decomposition  of  nitrosotriacetonamine 294    (/ 

Catalytic  decomposition  of  diazoacetic  ester 295 

Inversion  of  cane  sugar 296 

Catalyses  in  general 296 

Miscellaneous  methods 296 

XXI.  Applications 298 

General  reviews 299 

The  theory  of  titration 299 

General  considerations 304 

Subject  index  to  bibliography 310 

Bibliography 346 

Appendix 456 

Table  A.  Standard  values  for  calomel  electrodes 456 

Table  B.  Showing  the  relation  of  [H+]  to  pH 456 

Table  C.  Temperature  factors  for  concentration  chains 457 

Table  D.  Correction  of  barometer  reading  for  temperature 458 


8  i  CONTENTS 

Table  E.  Barometric  corrections  for  H-electrode  potentials 459 

ce  a 

Table  F.  Values  of  log  and  of  log multiplied  by  the  tem- 

1  —  oc  1— a 

perature  factors  for  concentration  chains  at  20°,  25°,  30°  and 

37?5C 460-461 

Table  G.  Ionization  constants 462-463 

Logarithms  of  numbers 464-465 

Index  of  authors  mentioned  in  the  text 467 

Index  of  Subjects 471 


PREFACE  TO  THE  FIRST  EDITION 

Poincare"  in  The  Foundations  of  Science  remarks,  "There  are 
facts  common  to  several  sciences,  which  seem  the  common  source 
of  streams  diverging  in  all  directions  and  which  are  comparable 
to  that  knoll  of  Saint  Gothard  whence  spring  waters  which  fer- 
tilize four  different  valleys." 

Such  are  the  essential  facts  of  electrolytic  dissociation. 

Among  the  numerous  developments  of  the  theory  announced 
by  Arrhenius  in  1887  none  is  of  more  general  practical  importance 
than  the  resolution  of  "acidity"  into  two  components — the 
concentration  of  the  hydrogen  ions,  and  the  quantity  of  acid 
capable  of  furnishing  this  ionized  hydrogen.  For  two -reasons  the 
hydrogen  ion  occupies  a  unique  place  in  the  estimation  of  stu- 
dents of  ionization.  First,  it  is  a  dissociation  product  of  the  great 
majority  of  compounds  of  biochemical  importance.  Second,  it  is 
the  ion  for  which  methods  of  determination  have  been  best 
developed.  Its  importance  and  its  mensurability  have  thus 
conspired  to  make  it  a  center  of  interest.  The  consequent  group- 
ing of  phenomena  about  the  activity  of  the  hydrogen  ion  is 
unfortunate  when  it  confers  undue  weight  upon  a  subordinate 
aspect  of  a  problem  or  when  it  tends  to  obscure  possibilities  of 
broader  generalization.  Nevertheless,  such  grouping  is  often  con- 
venient, often  of  immediate  value  and  frequently  illuminating. 
Especially  in  the  field  of  biochemistry  it  has  coordinated  a  vast 
amount  of  material.  It  has  placed  us  at  a  point  of  vantage  from 
which  we  must  look  with  admiration  upon  the  intuition  of  men 
like  Pasteur,  who,  without  the  aid  of  the  precise  conceptions 
which  guide  us,  handled  "acidity"  with  so  few  mistakes. 

In  the  charming  descriptions  of  his  experimental  work  Pasteur 
has  given  us  glimpses  of  his  discernment  of  some  of  the  effects  of 
"acidity"  in  biochemical  processes.  In  the  opening  chapter  of 
Studies  on  Fermentation  he  noted  that  the  relatively  high  acidity 
of  must  favors  a  natural  alcoholic  fermentation  in  wine,  while  the 
low  acidity  of  wort  induces  difficulties  in  the  brewing  of  beer. 
He  recognized  the  importance  of  acidity  for  the  cultivation  of 
the  bacteria  which  he  discovered  and  was  quick  to  see  the  lack  of 

9 


10  PREFACE   TO   FIRST   EDITION 

such  an  appreciation  in  his  opponents.  In  describing  that  process 
which  has  come  to  bear  his  name  Pasteur  remarks,  "It  is  easy 
to  show  that  these  differences  in  temperature  which  are  required 
to  secure  organic  liquids  from  ultimate  change  depend  exclusively 
upon  the  state  of  the  liquids,  their  nature  and  above  all  upon  the 
conditions  which  affect  their  neutrality  whether  towards  acids  or 
bases."  The  italics,  which  are  ours,  emphasize  language  which 
indicates  that  Pasteur  was  aware  of  difficulties  which  were  not 
removed  till  recently.  Had  Pasteur,  and  doubtless  others  of  like 
discernment,  relied  exclusively  upon  volumetric  determination  of 
acidity  they  would  certainly  have  fallen  into  the  pitfalls  which 
at  a  later  date  injured  the  faith  of  the  bacteriologist  in  the  meth- 
ods of  the  chemist.  Was  it  reliance  upon  litmus  which  aided 
him?  Perhaps  the  time  factor  involved  in  the  use  of  litmus 
paper,  which  is  now  held  as  a  grave  objection,  enabled  Pasteur 
to  judge  between  extremes  of  reaction  which  the  range  of  litmus 
as  an  indicator  in  equilibrium  does  not  cover.  At  all  events  he 
recognized  distinctions  which  we  now  attribute  to  hydrogen  ion 
concentrations.  Over  half  a  century  later  we  find  some  of 
Pasteur's  suggestions  correlated  with  a  marvelous  development 
in  biochemistry.  The  strongest  stimulus  to  this  development 
can  doubtless  be  traced  to  the  work  of  S0rensen  at  the  Carlsberg 
Laboratory  in  Copenhagen  and  not  so  much  to  his  admirable 
exposition  of  the  effect  of  the  hydrogen  ion  upon  the  activity  of 
enzymes  as  to  his  development  of  methods.  At  about  the  same 
time  Henderson  of  Harvard,  by  setting  forth  clearly  the  equilibria 
among  the  acids  and  bases  of  the  blood,  indicated  what  could  be 
done  in  the  realm  of  physiology  and  stimulated  those  researches 
which  have  become  one  of  the  most  beautiful  chapters  in  this 
science. 

Today  we  find  new  indicators  or  improved  hydrogen  electrode 
methods  in  the  physiological  laboratory,  in  the  media  room  of 
the  bacteriologist,  serving  the  analyst  in  niceties  of  separation 
and  the  manufacturer  in  the  control  of  processes.  The  material 
which  was  admirably  summarized  by  Michaelis  in  1914,  and  to 
which  Michaelis  himself  had  contributed  very  extensively,  pre- 
sents a  picture  whose  significance  he  who  runs  may  read.  There 
is  a  vast  field  of  usefulness  for  methods  of  determining  the  hydro- 
gen ion.     There  is  real  significance  in  the  fruits  so  far  won. 


PREFACE   TO   FIRST   EDITION  11 

There  remain  many  territories  to  explore  and  to  cultivate.  We 
are  only  at  the  frontier. 

In  the  meantime  it  will  not  be  forgotten  that  our  knowledge  of 
the  hydrogen  ion  is  an  integral  part  of  a  conception  which  has 
been  under  academic  study  for  many  years  and  that  the  time  has 
come  when  the  limitations  as  well  as  certain  defects  are  plainly 
apparent.  While  there  is  now  no  tendency  nor  any  good  ground 
to  discredit  the  theory  of  electrolytic  dissociation  in  its  essential 
aspects,  there  is  dissatisfaction  over  some  of  the  quantitative 
relationships  and  a  demand  for  broader  conceptions.  It  requires 
no  divination  to  perceive  that  while  we  remain  without  a  clear 
conception  of  why  an  electrolyte  should  in  the  first  instance 
dissociate,  we  have  not  reached  a  generalization  which  can  cover 
all  the  points  now  in  doubt.  Perhaps  the  new  developments  in 
physics  will  furnish  the  key.  When  and  how  the  door  will  open 
cannot  be  foreseen ;  but  it  is  well  to  be  aware  of  the  imminence  of 
new  developments  that  we  may  keep  our  data  as  pure  as  is  con- 
venient and  emphasize  the  experimental  material  of  permanent 
value.  We  may  look  forward  to  continued  accumulation  of 
important  data  under  the  guidance  of  present  conceptions,  to 
distinguished  services  which  these  conceptions  can  render  to 
various  sciences  and  to  the  critical  examination  of  the  material 
gathered  under  the  present  regime  for  the  elements  of  permanent 
value.  These  elements  will  be  found  in  the  data  of  direct  experi- 
mentation, in  those  incontrovertible  measurements  which,  though 
they  be  but  approximations,  have  immediate  pragmatic  value 
and  promise  to  furnish  the  bone  and  sinew  of  future  theory.  In 
the  gathering  of  such  data  guiding  hypotheses  and  coordinating 
theories  are  necessary  but  experimental  methods  are  vital. 

The  time  seems  to  have  come  when  little  of  importance  is  to 
be  accomplished  by  assembling  under  one  title  the  details  of 
the  manifold  applications  of  hydrogen  electrode  and  indicator 
methods.  It  would  be  pleasing  to  have  in  English  a  work  com- 
parable in  scope  with  Michaelis'  Die  W asserstoffionenkonzentra- 
tion;  but  even  in  the  short  years  since  the  publication  of  this 
monograph  the  developments  in  special  subjects  have  reached 
such  detail  that  they  must  be  redispersed  among  the  several  sci- 
ences, and  made  an  integral  part  of  these  rather  than  an  unco- 
ordinated treatise  by  themselves.     There  remains  the  need,  for  a 


12  PREFACE   TO    FIRST   EDITION 

detailed  exposition,  under  one  cover,  of  the  two  methods  which 
are  in  use  daily  by  workers  in  several  distinct  branches  of  bio- 
logical science.  It  is  not  because  the  author  feels  especially 
qualified  to  make  such  an  exposition  that  this  book  is  written, 
but  rather  because,  after  waiting  in  vain  for  such  a  book  to 
appear,  he  has  responded  sympathetically  to  appeals,  knowing 
full  well  from  his  own  experience  how  widely  scattered  is  the 
information  under  daily  requisition  by  scores  of  fellow  workers. 

For  the  benefit  of  those  to  whom  the  subject  may  be  new 
there  is  given  in  the  last  chapter  a  running  summary  of  some  of 
the  principal  applications  of  the  methods.  This  is  written  in 
the  form  of  an  index  to  the  bibliography,  a  bibliography  which 
is  admittedly  incomplete  for  several  topics  and  unbalanced  in 
others,  but  which,  it  is  believed,  contains  numerous  nuclei  for 
the  assembling  of  literature  on  various  topics. 

The  author  welcomes  this  opportunity  to  express  his  apprecia- 
tion of  the  broad  policy  of  research  established  in  the  Dairy  Divi- 
sion Laboratories  of  the  Department  of  Agriculture  under  the 
immediate  administration  of  Mr.  Rawl  and  Mr.  Rogers.  Their 
kindness  and  encouragement  have  made  possible  studies  which 
extend  beyond  the  range  of  the  specialized  problems  to  which 
research  might  have  been  confined  and  it  is  hoped  that  the  bread 
upon  the  waters  may  return.  To  Dr.  H.  A.  Lubs  is  due  the  credit 
for  studies  on  the  synthesis  of  sulfonphthalein  indicators  which 
made  possible  their  immediate  application  in  bacteriological 
researches  which  have  emanated  from  this  laboratory.  Acknowl- 
edgment is  hereby  made  of  the  free  use  of  quotations  taken 
from  the  paper  The  Colorimetric  Determination  of  Hydrogen  Ion 
Concentration  and  Its  Applications  in  Bacteriology  published  in 
the  Journal  of  Bacteriology  under  the  joint  authorship  of  Clark 
and  Lubs. 

The  author  thanks  his  wife,  his  mother,  Dr.  H.  W.  Fowle  and 
Dr.  H.  Connet  for  aid  in  the  correction  of  manuscript  and  proof, 
and  Dr.  Paul  Klopsteg  for  valuable  suggestions. 

It  is  a  pleasure  to  know  that  the  publication  of  the  photograph 
of  Professor  S.  P.  L.  S0rensen  of  the  Carlsberg  Laboratory  in 
Copenhagen  will  be  welcomed  by  American  biochemists  all  of 
whom  admire  his  work. 

Chevy  Chase,  Maryland 
March  17,  1920 


PREFACE  TO  THE  SECOND  EDITION 

The  first  edition  of  this  book  was  offered  to  fellow  workers  for 
the  reasons  stated  in  the  preface.  The  rapid  exhaustion  of  two 
printings  has  revealed  the  extent  of  the  demand  for  information 
upon  the  topics  discussed;  but  it  has  also  brought  to  the  author  a 
disquieting  realization  of  the  responsibility  assumed  at  the  first 
venture,  and  regret  that  his  preoccupation  in  a  distinctive 
although  allied  realm  of  research  has  prevented  investigations  which 
might  have  contributed  data  for  a  more  complete  second  edition. 
This  same  preoccupation  may  be  offered  as  an  excuse  for  the 
deficiencies  in  the  bibliography  and  its  classification.  Over  900 
new  references  have  been  added  to  the  eleven  hundred  odd  said 
to  be  in  the  first  edition;  but,  when  it  is  realized  that  much  of  the 
newer  information  is  contained  in  papers  neither  the  title  nor 
general  subject  of  which  would  indicate  that  hydrogen  ion  con- 
centrations have  been  considered,  it  will  be  appreciated  that  the 
task  of  the  bibliographer  requires  more  time  than  an  investigator 
can  afford.  Indeed  it  will  not  be  long  before  it  will  be  as  difficult 
to  trace  this  information  as  it  has  become  to  trace  all  the  effects 
of  temperature.  In  certain  fields  of  investigation  "pH"  is  becom- 
ing almost  as  common  as  "°C."  Were  it  not  that  the  introduction 
of  a  new  symbol  would  introduce  confusion  we  would  wish  that 
the  special  interpretation  of  pH  given  in  Chapter  XVII  of  the 
first  edition  (Chapter  XIX,  this  edition)  could  be  symbolized  by 
°S  (degrees  S0rensen). 

Certain  chapters  of  the  first  edition  have  been  rewritten  and 
all  have  been  expanded  to  bring  the  book  up  to  date  and  to  meet 
the  very  helpful  suggestions  given  in  the  generous  reviews  of  the 
first  edition,  or  by  personal  correspondence.  It  has  been  advis- 
able, however,  either  to  balance  one  suggestion  against  another 
or  to  rely  upon  one's  own  judgment  to  maintain  a  balance  in  the 
general  treatment. 

The  question  of  a  change  of  treatment  to  conform  throughout 
to  the  "activity"  concept  has  been  given  serious  consideration. 
The  author  has  been  counseled  by  experienced  teachers  not  to 
attempt  such  a  change,  but  his  chief  reason  for  definitely  rejecting 

13 


14  PREFACE   TO    SECOND    EDITION 

the  -proposal  is  simply  that  most  of  the  data  in  use  are  still  in 
terms  of  the  older  conceptions.  In  the  recasting  of  this  data  a 
great  deal  of  new  experimental  material  must  be  collected  and 
the  newer  conceptions  must  be  stabilized.  Anything  short  of  a 
thorough  revision  of  existing  data  would  be  but  to  cover  the 
subject  with  a  thin  veneer  giving  the  appearance  rather  than 
the  substance  of  an  up-to-date  treatment. 

The  author  is  indebted  to  so  many  people  for  helpful  sugges- 
tions that  it  would  appear  ungracious  to  mention  but  a  few.  How- 
ever, due  credit  must  be  given  to  Dr.  Barnett  Cohen  for  pains- 
taking correction  of  proof,  to  Miss  Florence  Lansdale  for  clerical 
assistance  and  to  the  publishers  for  their  unfailing  and  courteous 
cooperation. 

Chevy  Chase,  Maryland 
May  22,  1922 


CHAPTER  I 

Introduction — Some  General  Relations  Among  Acids 

and  Bases 

In  a  country  rich  in  gold  observant  wayfarers  may  find  nuggets  on 
their  path,  but  only  systematic  mining  can  provide  the  currency 
of  nations. — F.  Gowland  Hopkins. 

Why  certain  solvents  such  as  water  should  cause  or  permit 
the  splitting  of  a  compound  into  electrically  charged  bodies, 
called  ions,  has  not  yet  been  very  clearly  explained.  That  they 
do  has  been  demonstrated  with  reasonable  certainty.  The  evi- 
dences are  described  in  texts  of  physical  chemistry  and  will  not 
be  reviewed  here,  except  as  they  are  revealed  in  the  verification 
of  the  laws  of  chemical  equilibria  among  electrolytes. 

That  aspect  of  electrolytic  dissociation  which  is  of  special 
interest  to  us  may  be  conveniently  pictured  as  follows. 

A  chemical  element  is  conceived  to  be  an  aggregate  of  unit, 
negative,  electrical  charges  (electrons)  grouped  at  relatively 
enormous  distances  about  a  central,  neutralizing  nucleus  of 
positive  electricity.  The  numerical  value  of  this  nucleus,  in 
terms  of  the  number  of  electrons  required  for  neutralization,  and 
the  geometrical  configuration  of  the  positions  of  the  surrounding 
electrons  are  supposed  to  distinguish  the  several  elements. 

Certain  of  the  electrons  are  but  weakly  incorporated  in  the 
planet-like  system  of  certain  elements.  When  such  an  electron 
has  escaped,  the  element  is  left  with  a  unit  excess  of  positive 
electricity.  It  is  then  a  positive  ion,  a  cation,  having  distinctive 
properties. 

If  an  element  is  so  constituted  that  it  can  hold  an  extra  electron, 
the  extra  charge  gives  it  new  characteristics.  The  negatively 
charged  element  is  called  an  anion. 

Certain  compounds  such  as  HC1  are  made  up  of  elements  of 
the  two  types  mentioned  above.  On  electrolytic  dissociation  HC1 
oreaks  up  in  such  a  way  that  the  hydrogen  atom  loses  an  electron 
ind  this  is  taken  up  by  the  chlorine  atom.     HC1,  thus,  dissociates 

15 


16  THE    DETERMINATION    OF   HYDROGEN    IONS 

into  the   positively  charged  hydrogen  ion  and  the  negatively 
charged  chlorine  ion.    The  process  may  be  represented  as  follows: 

HC1?±H+  + Cl- 
in the  case  of  complex  compounds  such  as  acetic  acid  a  similar 
exchange  of  an  electron  occurs.     The  group  CH3COO  acts  as  a 
unit  and  when  negatively  charged  becomes  the  acetate  anion. 

Frequently  an  element  or  group  can  lose  or  acquire  several  elec- 
trons. For  instance  Ca++  is  the  divalent  cation  of  calcium  and 
SO4  is  the  divalent  anion  of  the  sulfate  group — called  divalent 
because  there  are  concerned  two  of  those  electrons  which  are  sup- 
posed to  be  intimately  connected  with  the  phenomenon  of  valency. 

In  passing  it  is  interesting  to  note  that  the  hydrogen  ion  is 
unique.  The  element  hydrogen  is  supposed  to  have  but  one 
electron  to  the  atom.  When  this  is  lost  there  is  left  the  hydrogen 
ion,  a  lone  unit,  positive  charge. 

Now  this  pictorial  conception  of  the  structure  of  elements, 
while  pregnant  with  possibilities,  must  not  be  considered  vital 
to  the  subject  at  hand.  The  one  aspect  which  is  vital  is  that 
there  occur  dissociations  whereby  an  element  or  group  becomes 
electrically  charged — positively  or  negatively,  as  the  case  may  be. 
It  is  the  electrical  charge  which  turns  an  element  or  group  into  a 
virtually  new  body  and  at  the  same  time  furnishes  a  handle,  as 
it  were,  with  which  we  may  lay  hold  on  it  by  electrical  devices. 

On  the  other  hand  the  electrical  charge  does  not  prevent  a 
limited  application  to  ions  of  the  laws  of  chemical  equilibria. 
Indeed  it  is  among  dilute  solutions  of  certain  electrolytically 
dissociated  compounds  that  there  have  been  found  the  most 
exact  data  supporting  the  laws  of  chemical  equilibria. 

It  is  with  these  laws  of  chemical  equilibria  that  we  are  chiefly 
concerned  when  dealing  with  the  measurement  of  and  the  effects 
of  hydrogen  ion  concentration.  Therefore,  if  electrolytic  ioni- 
zation be  granted  as  a  fact,  it  is  only  necessary  to  sketch  the 
concept  of  chemical  equilibrium  before  coming  to  the  simple,  if 
somewhat  detailed  account  of  the  special  manner  in  which  the 
concept  is  applied  to  acid-base  equilibria. 

Consider  an  acid  of  the  type  HA  dissociating  into  tue  cation 
H+  (hydrogen  ion)  and  the  anion  A-.  The  process  may  be 
expressed  as  follows: 

HA  ^±  H+  +  A"  (1) 


GENERAL   RELATIONS    AMONG   ACIDS   AND   BASES  17 

Arrows  are  used  to  indicate  that  the  process  is  reversible, — 
that  among  the  large  number  of  anions  and  cations  present  in  a 
given  volume  some  are  recombining  to  form  HA  the  while  a 
portion  of  the  HA  molecules  are  dissociating. 

This  concept  of  a  "reaction"  as  labile,  continuous,  reversible 
is  of  profound  importance.  So  long  as  analysts  are  content  to 
balance  the  two  sides  of  a  written  reaction  with  regard  only  to 
the  stoichiometrical  relations,  it  is  convenient  to  use  the  equation 
sign  and  to  forget  the  reality  implied  in  the  use  of  arrows.  Reac- 
tions do  not  go  to  completion  and  only  approach  completion 
when  by  design  or  chance  the  proper  conditions  are  supplied. 
This  reversibility  of  chemical  reactions  displays  a  world  in  flux. 
From  it  the  "everlasting  hills"  cannot  escape;  but  upon  it  life  bal- 
ances its  intricate  organization.  Often  this  is  done  so  nicely  that 
the  life  of  certain  organisms  is  almost  immortal. 

In  this  interminable  interplay  of  chemical  reactions  there  occur 
situations  when  on  the  statistical  average  a  given  reaction  is  pro- 
ceeding no  faster  in  one  direction  than  in  the  other.  In  such 
circumstances  a  chemical  equilibrium  is  said  to  occur.  Let  us 
formulate  in  as  simple  a  way  as  possible  the  condition  of  a  chemical 
equilibrium. 

Let  brackets  placed  about  a  symbol  indicate  concentration  of 
the  bracketed  "species."  Thus  [HA]  represents  the  concentration 
of  the  residual,  undissociated  acid  HA.  Throughout  the  following 
discussions  we  shall  always  let  it  be  implied  that  by  "concentra- 
tion" is  meant  molar  concentration.  A  molar  solution  is  one 
containing  in  one  litre  of  solution  that  number  of  grams  of  the 
indicated  substance  which  is  equal  to  its  formula  weight. 

In  equation  (1)  the  rate  at  which  the  concentration  [HA]  is 
being  diminished  because  of  the  ionization  may  depend  upon 
several  physical  conditions.  To  know  these  is  unnecessary  for 
the  purpose  at  hand  if  we  may  assume  that  their  effect  on  the 
individual  molecules  of  HA  is  constant  on  the  statistical  average. 
Then,  obviously,  the  rate  at  which  reaction  (1)  proceeds  from 
left  to  right  will  depend  upon  the  concentration  of  HA  and  some 
constant  factor  which  will  be  called  ki. 

Velocity  left  to  right  =  ki  [HA]  (2) 

The  velocity  of  the  reverse  reaction  wherein  the  ions  recombine 
to  form  HA  might  be  supposed  to  be  dependent  only  upon  the 


18  THE   DETERMINATION   OP   HYDROGEN   IONS 

rate  at  which  the  ions  in  their  thermal  agitation  collide.  But  it 
is  difficult  to  say  what  degree  of  approach  is  necessary  for  com- 
bination or  what  other  conditions  must  be  fulfilled  before  the 
combination  can  be  considered  to  have  taken  place.  It  is  much 
safer  then  to  assume  only  that  some  degree  of  meeting  is  necessary, 
that  some  average  state  is  to  be  considered  virtual  combination 
and  that  the  physical  factors  bringing  about  this  state  are,  on 
the  statistical  average,  constant.  Here  again  then  we  ascribe 
the  velocity  of  the  reaction  first  to  a  factor  dependent  solely 
upon  the  numbers  of  ions  concerned  [concentration]  and  second 
another  factor  embracing  all  the  known  and  unknown  influences, 
exclusive  of  concentration.  Suppose  then  that  we  start  with 
equal  numbers  of  H+  ions  and  A~  ions  and  double  the  concen- 
tration of  H+.  Evidently  the  number  of  collisions  of  H+  ions 
with  A-  ions  will  double.  Likewise,  if  [A-]  is  doubled,  the  number 
of  collisions  of  A-  with  H+  ions  will  be  doubled.  If  both  are 
doubled,  the  collisions  are  quadrupled.  Consequently  the  velocity 
of  association,  in  so  far  as  it  is  dependent  upon  the  concentrations 
of  the  reactants,  is  proportional  to  the  product  of  these  concen- 
trations. Introducing  the  unknown  proportionality  factor  repre- 
senting the  constant  effect  of  all  physical  influences,  we  have : 

Velocity  right  to  left  =  k2  [H+]  [A-].  (3) 

We  have  already  said  that  the  state  of  equilibrium  occurs  when 
the  velocity  of  the  reaction  in  one  direction  equals  the  velocity  in 
the  reverse  direction.  Then  at  once  by  combining  (2)  and  (3) 
we  have: 

[H+]  [Aj  _  kx  , 

[HA]      ~  k2  ~  Ka  W 

For  the  ratio  of  two  constants  there  is  substituted  in  (4)  another 
constant,  Ka,  known  as  the  equilibrium  constant.  This  equilib- 
rium constant  when  applied  to  electrolytes  is  known  as  the 
ionization  or  dissociation  constant.1 

1  It  should  be  particularly  noted  that  in  equation  (4)  the  brackets 
symbolize  the  concentrations  occurring  at  the  equilibrium  state.  When- 
ever numerical  values  are  to  be  introduced  it  is  to  be  assumed  that  there 
will  be  employed  the  same  unit  of  concentration  that  was  used  in  the  experi- 
mental derivation  of  Ka,  and  also  the  conventional  form  of  the  ratio  with 
the  ions  in  the  numerator. 


GENERAL   RELATIONS   AMONG   ACIDS   AND    BASES  19 

Since  equation  (4)  deals  with  the  active  masses  of  the  reactants 
it  is  a  special  application  of  the  so-called  law  of  mass  action  which 
states  that  the  velocity  of  a  reaction  is  proportional  to  the  product 
of  the  concentrations  of  the  reactants. 

Using  equation  (4)  for  a  particular  acid  it  will  be  seen  by  inspec- 
tion of  the  equation  that  if  [H+]  is  increased,  as  by  the  addition 
of  another  acid,  there  must  be  a  readjustment  of  either  [A-]  or 
[HA]  or  both  to  keep  Ka  constant.  Likewise  if  [A~]  should  be 
increased  by  the  addition  of  a  highly  dissociating  salt  of  the  acid  in 
question,  there  would  be  a  readjustment  of  either  [H+]  or  [HA]  or 
both  to  keep  Ka  constant.  Thus  the  independent  alteration  of 
the  concentration  of  any  one  of  the  species  included  in  the  equi- 
librium equation  causes  a  displacement  of  the  equilibrium  to  a 
new  position.  This  illustrates  how  difficult  it  is  to  keep  track  of 
the  affair  unless  use  is  made  of  the  simple  algebraic  relations. 

If  the  acid  alone  be  present,  [H+]  =  [A-].  Substituting  [H+] 
for  [A-]  and  solving  equation  (4)  for  [H+]  we  have 


[H+]  =  VKa  [HA] 

If  the  acid  is  so  weak  that  practically  all  is  in  the  undissociated 
form,  no  great  error  is  made  in  putting  [HA]  equal  to  the  con- 
centration [S]  of  the  total  acid.    Then  [H+]  =  VKJS]". 

In  general  it  can  be  shown  that  for  any  reaction  such  as 

A  +  B  +  C  +  .  .  .  .  .  ;=±  A'  +  B'  +  C  + 

the  equilibrium  condition  is: 

[A]  [B]  [C]   .  .  . 


[A']  IB']  [CI 


=  k 


From  the  assumptions  introduced  in  the  argument  it  is  evident 
that  the  equilibrium  constant  will  hold  good  only  so  long  as  there 
are  maintained  constant  those  physical  conditions  which  affect 
the  velocity  of  a  reaction  in  one  direction  or  the  reverse.  A 
change  in  temperature  will  alter  the  "constant,"  but  not  to  such 
an  extent  as  will  a  change  in  solvent.  With  due  regard  for  such 
matters  we  may  regard  the  equilibrium  constant  as  a  number 
characteristic  of  a  given  reaction  at  the  equilibrium  state. 

In  the  derivation  of  the  equilibrium  equation  we  have  employed 
as  an  example  the  electrolytic  dissociation  of  an  acid.     We  may 


20 


THE   DETERMINATION    OF   HYDROGEN   IONS 


now  state  that  all  substances  capable  of  yielding  hydrogen  ions 
must  be  considered  as  having  an  acidic  nature  and  their  conduct 
in  solution  must  be  governed  by  the  equilibrium  equation. 

With  the  ionization  constant  denned  we  are  prepared  to  give 
quantitative  significance  to  comparative  "strengths"  among  acids. 
Inspection  of  equation  (4)  shows  at  once  that  if  Ka  is  large  the 
numerator  of  the  left  hand  side  must  be  large  in  relation  to  the 
denominator.  In  other  words  an  acid  having  a  relatively  high 
Ka  value  will,  if  left  to  itself  in  solution,  tend  toward  a  high  degree 
of  dissociation.  A  given  over-all  concentration  of  an  acid  with 
high  dissociation  constant  will  furnish  a  higher  concentration  of 
hydrogen  ions  than  will  the  same  over-all  concentration  of  an 
acid  with  low  dissociation  constant.  Thus  the  value  of  Ka  at 
once  indicates  the  "strength"  of  an  acid  so  far  as  "strength"  is 
measurable  in  terms  of  ionization. 

In  the  following  table  are  given  a  few  dissociation  constants 
of  acids  and  also  of  bases. 

TABLE  1 

Showing  acidic  and  basic  dissociation  constants  and  their  relation  to  a  rough 

classification  of  acids  and  bases 


CLASS 

COMPOUND 

DISSOCIATION  CONSTANT 

Strong  acid 

Hydrochloric 
Oxalic  (first  H) 
Acetic 
Boric 

Sodium  hydroxid 
Ammonium  hydroxid 
Aniline 

Not  well  defined 

Weak  acid 

1.1  X  10"1 
1.8  X  10_s 

Very  weak  acid 

6.5  X  10_1° 

Strong  base 

Not  well  defined 

Weak  base 

1.8  X  10-s 

Very  weak  base 

4.6  X  10~10 

The  dissociation  of  bases  will  now  be  considered.  Just  as  a 
substance  ionizing  to  give  hydrogen  ions  is  called  an  acid  so  a 
substance  which  ionizes  to  give  hydroxyl  ions  (OH-)  is  called 
a  base. 

The  reversible  reaction  NaOH  ^  Na+  +  OH~  may  be  written 
as  BOH  ^±  B+  +  OH-  where  B  represents  any  monovalent 
metal.  This  reaction  may  be  treated  in  precisely  the  same  way 
that  reaction  (1)  was  treated.     The  equilibrium  condition  is: — 


[B+]  [QH- 
[BOH] 


=  Kb 


(5) 


GENERAL  RELATIONS  AMONG  ACIDS  AND   BASES  21 

Just  as  the  value  of  Ka  is  characteristic  of  a  given  acid  so  is 
the  value  of  Kb  characteristic  of  a  given  base. 

A  very  important  relationship  between  acids  and  bases  in 
aqueous  solution  is  brought  about  by  the  conduct  of  water. 
It  dissociates  into  the  hydrogen  ion  (H+)  characteristic  of  acids 
and  the  ion  characteristic  of  bases,  OH-,  called  the  hydroxyl  ion. 
The  equilibrium  of  the  reversible  reaction  HOH  ^±  H+  +  OH-  is 
represented  by 

[H+]  [OH-]  _ 
[HOH] 

Because  the  concentration  of  the  undissociated  water  is  so 
large  in  relation  to  the  dissociation  products,  [HOH]  will  not  be 
changed  appreciably  by  the  slight  dissociation.  [HOH]  may 
therefore  be  considered  a  constant  and  combined  with  k.  Then 
the  above  equation  becomes: 

[H+]  [OH-]  -  Kw.  (6) 

It  follows  from  this  equation  that,  no  matter  how  concentrated 
the  hydroxyl  ions  may  be,  there  must  remain  sufficient  hydrogen 
ions  to  satisfy  the  above  relation.2  This  permits  us  to  speak  of 
the  hydrogen  ion  concentration  of  alkaline  solutions  and,  as  will 
be  shown  presently,  to  construct  a  scale  of  acidity-alkalinity  in 
which  we  do  not  discriminate  between  hydrogen  and  hydroxyl 
ion  concentration. 

Starting  from  equations  (4),  (5)  and  (6),  applying  certain 
approximations  and  then  using  graphic  methods  of  presentation 
we  can  present  a  generalized  picture  of  the  conduct  of  acids  and 
bases  similar  to  that  first  used  by  Henderson  (1908).  The  final 
simplicity  of  the  picture  warrants  what  may  at  first  appear  to  be 
a  complicated  reconstruction  of  the  above  equations. 

In  order  to  emphasize  the  hydrogen  ion  concentration  as  the 
quantity  in  equation  (4)  with  which  the  other  species  keep  in 
adjustment,  let  us  rewrite  equation  (4)  as  follows: 

1  [A-] 


[H+]       Ka[HA] 

*  Kw  =  10-14.    If  in  an  alkaline  solution  the  concentration  of  hydroxyl 

*.  Kw  in-14 

ions  is  0.01  normal  (10~2),  [H+]  =  : — ^-r  =  =—  =  10"12  N. 

[OH"]       10~2 


22 


THE  DETERMINATION  OF  HYDROGEN  IONS 


We  choose  the  form  which  will  give  the  reciprocal  of  [H+] 
because  we  shall  have  to  make  use  of  the  logarithm  of  this  value 
under  the  symbol  pH  for  reasons  which  will  appear  later.  For 
the  present  let  it  be  granted  that  it  will  be  found  convenient  to 

use  log  rather  than  [H+].     Taking  the  logarithm  of  each 

[H+J 

side  of  the  above  equation  we  have 


i      i       .     i,  .     [Ai 

log •  =  log 1-  log ; 

[H+]  Ka  *  [HA] 


(7) 


PH 


%J 

s. 

* 

I        A 

■ 

( 

>                 i 

*        10 

cc 

Fig.  1.  Comparison  of  Experimental'  Titration  Curve  of  Acetic  Acid 
with  Theoretical  Approximation 

With  the  use  of  this  equation  we  can  chart  some  important 
relationships.  Let  it  first  be  applied  to  what  may  be  called 
"titration  curves." 

Suppose  we  titrate  10  cc.  of  0.2n  acetic  acid  with  0.2n  sodium 
hydroxid.  Ordinarily  no  attention  would  be  given  to  the  state 
of  the  solution  until  the  so  called  "end  point"  of  the  titration 
were  reached.  In  the  present  instance  we  shall  follow  the  course 
of  the  titration  from  the  beginning  by  determining  after  each 
addition  of  alkali  the  hydrogen  ion  concentration. 


GENERAL   RELATIONS   AMONG   ACIDS   AND    BASES 


23 


The  experimental  curve  is  plotted  in  figure  1.  Let  us  com- 
pare it  with  the  values  obtained  by  the  use  of  equation  (7) . 

In  the  first  place  acetic  acid  is  classed  among  the  moderately 
weak   acids.     Its    dissociation    constant   as    given   in   Landolt- 

Bornstein  is  1.82  X  10"5  at  18°C.     Hence  log  =r  =  4.74.    Be- 

-t»-a 

TABLE  2 

Comparison  of  log  1/[H+]  for  acetic  acid-sodium  acetate  calculated  by  means  of 

the  approximation  formulated  in  equation  (8)  and  determined 

experimentally  by  Walpole 


N/5  NaOH 

RATIO 

[salt] 
[acid] 

LOG  RATIO 

log  1/Ka 

LOG  1/[H+] 
CALCULATED 

LOG  1/[H+] 
WALPOLE 

cc. 

0.20 

9.00 

-1.69 

4.74 

3.05 

3.08 

0.25 

0.020 

-1.59 

4.74 

3.15 

3.15 

0.30 

0.026 

-1.51 

4.74 

3.23 

3.20 

0.40  . 

0.031 

-1.38 

4.74 

3.36 

3.32 

0.50 

0.042 

-1.28 

4.74 

3.46 

3.42 

0.75 

0.053 

-1.09 

4.74 

3.65 

3.59    . 

1.0 

0.081 

-0.95 

4.74 

3.79 

3.72 

2.0 

0.111 

-0.60  m 

4.74 

4.14 

4.05 

3.0 

0.250 

-0.37 

4.74 

4.37 

4.27 

4.0 

0.429 

-0.18 

4.74 

4.56 

4.45 

5.0 

0.667 

0.00 

4.74 

4.74 

4.63 

6.0 

1.000 

+0.18 

4.74 

4.92 

4.80 

7.0 

1.500 

+0.37 

4.74 

5.11 

4.99 

7.5 

2.33 

+0.48 

4.74 

5.22 

5.09 

8.0 

3.00 

+0.60 

4.74 

5.34 

5.23 

8.5 

4.00 

+0.75 

4.74 

5.49 

5.37 

9.0 

5.67 

+0.95 

4.74 

5.69 

5.57 

9.5 

19.00 

+1.28 

4.74 

6.02 

5.89 

9.625 

25.67 

+1.41 

4.74 

6.15 

6.02 

9.75 

39.00 

+1.59 

4.74 

6.33 

6.21 

9.875 

79.00 

+1.90 

4.74 

6.64 

6.52 

cause  of  the  small  dissociation  of  acetic  acid  (less  than  2  per  cent 
in  0.2n  solution  even  with  no  acetate  present)  the  concentration 
of  the  undissociated  residue  [HAc]  is  approximately  equal  to  the 
concentration  of  the  total  acetic  acid.  It  is  characteristic  of  the 
alkali  salts  of  acids  that  they  are  very  highly  dissociated.  There- 
fore, when  sodium  hydroxid  is  added  to  the  acetic  acid  solution, 
the  resulting  sodium  acetate  furnishes  the  greater  amount  of  the 


24  THE   DETERMINATION   OF   HYDROGEN   IONS 

total  acetate   (Ac~)   ions.     As  an  approximation  therefore  we 

[A-]  [salt] 

may  substitute  for  the  ratio  7777",  in  equation  (7)  the  ratio  7 — —  • 

[HA]  [acid] 

Equation  (7)  then  becomes: 

log  J_  =log-L  +  log^-j.  (8) 

*[H+J  &Ka         *[acid] 

[  salt] 
In  table  2  are  given  the  ratios  r — 77.  calculated  from  the  num- 

[acid] 

ber  of  cubic  centimeters  of  0.2n  alkali  added  to  10  cc.  of  0.2n 

acetic  acid.     Then  follow  the  logarithms  of  these  ratios,  the  value 

of  log  z?~  for  acetic  acid,  and  log  7777;  calculated  from  these  data 

-TV  a  L-H-    J 

by  means  of  equation  (8).     Finally  in  the  last  column  are  given 

the  values  of  log  ,777;  calculated  by  Walpole  (1914)  from  his 

l**TJ 
hydrogen    electrode    measurements.     The    experimental   values 

pH  =  log  7777;  are  plotted  in  figure  1  as  circles  while  the  values 
LJfcr«-j 

calculated  by  means  of  the  approximation  equation  (8)  are  on  the 

unmarked  line.     There  is  evidently  a  substantial  agreement  with 

a  more  or  less  regular  discrepancy  which  remains  to  be  explained. 

The  discrepancy  may  be  ascribed  in  part  to  the  assumption  that 

the  salt  is  wholly  dissociated  and  that  it  is  entirely  responsible 

for  the  anions  of  equation  (7).     If  there  be  applied  a  correction 

for  the  partial  dissociation  of  the  acetate,  there  is  obtained  a 

much  closer  agreement. 

But  even  this  correction  does  not  take  into  consideration  cer- 
tain minor  points,  and  it  leaves  untouched  both  the  accuracy  with 
which  Ka  has  been  determined  and  the  comparability  of  data 
obtained  by  widely  different  methods  which  are  often  applied 
(sometimes  uncritically)  in  making  such  calculations  as  those 
indicated  above. 

We  shall  proceed  with  the  approximate  treatment  to  bring  out 
certain  more  general  relations,  and  shall  leave  to  Chapter  XXI 
their  further  application  to  ordinary  titrations. 

[salt]  1 

In  equation  (8)  when  the  ratio  f — rrr  equals  one,  log  J777;  = 

log  77      Then  [H+]  =  K.. 


GENERAL   RELATIONS   AMONG   ACIDS   AND    BASES  25 

In  other  words  the  middle  portion  of  the  titration  curve  of  a 
particular  acid  lies  at  ("near"  if  we  are#  to  be  strict)  a  point 
where  the  hydrogen  ion  concentration  is  numerically  equal  to  the 
dissociation  constant.3 

Thus  if  one  wishes  a  solution  of  [H+]  =  1  X  10~5,  an  acid  with 
dissociation  constant  close  to  this  value  is  selected  and  mixed 
with  the  proper  amount  of  its  alkali  salt. 

Or  to  look  at  the  matter  from  another  point  of  view,  if  we 
determine  the  half  transformation  point  in  the  titration  of  a 
weak  acid,  we  know  approximately  the  dissociation  constant  of 
the  acid. 

A  similar  set  of  relationships  can  be  constructed  for  bases. 

Instead  of  putting  the  fundamental  equation  (4)  into  the 
form  which  we  have  utilized  in  following  titration  curves  it  is 
sometimes  advantageous  to  use  the  following  development. 

Transforming  (4)  we  have : 

[A-]  _    Ka 
[HA]       [H+] 

Now  let  us  represent  the  concentration  of  the  total  acid  by  [S]. 
Then  the  concentration  of  [HA]  will  be : 

[HA]  =  [S]  -  [A-] 

[A~]  Ka 

[S]-[Ai  [H+] 
or 

[A-]  Ka 


[S]        Ka  +  [H+] 

[A-] 
The  ratio  -rrr-  is  the  ratio  of  the  dissociated  acid  to  the  total  acid 
L»J 

present  in  the  solution.     This  ratio  may  be  represented  by  a. 
Hence, 

Ka 


Ka  +  [H+] 


(9) 


3  There  is  implied  in  this  the  maintenance  of  the  customary  unit  of 
concentration.    Cf.  page  18. 


26  THE   DETERMINATION   OF   HYDROGEN   IONS 


/  1   \  /^  — \ 

Since  we  are  interested  in  log  rrrp:  or  pH  rather  than  [H+],  because 

of  the  resultant  simplification  of  chart  representations  and  because 
of  other  reasons  which  will  appear  later,  we  may  recast  equation 
(9)  and  taking  the  logarithm  of  each  side  we  have : 

11  ot 

log =  log h  log  — (10) 

*  [H+]  *  K.  *  (1  -  «) 

Plotting  log }  which  is  pH,  against  «,  and  expressing  «  as 

[H+J 

percentage  dissociation,  there  is  obtained  a  curve  such  as  A  or  B 
in  figure  2.     Such  curves  are  identical  in  form,  the  form  being 

Ot  * 

determined  by  the  ratio  — •     Their  position  on  the  pH  axis 

(1  -  «) 
is  determined  by  the  value  of  the  dissociation  constant  in  the 

expression  log  — 

Since  (10)  is  useful  in  plotting  type  curves  a  table  of  values  for 

log is  given  in  the  appendix  (p.  460). 

1  —  a 


(11) 


In  a  similar  way  we  arrive  at  the  relation  for  bases : 

a=  Kb 

"  Kb  +  [OH-] 
or 

logfOHi^log1^1"00-  (12) 

a 

But  since  we  wish  to  deal  uniformly  with  log  jTT^f,  which  is  pH, 

rather  than  with  the  hydroxyl  ion  concentration  or  any  direct 
function  thereof,  we  shall  introduce  the  water  equilibrium,  equa- 
tion (6).    Then  (12)  becomes 

logJEz.  =  log?EiiL^ 

[H+]  « 

or 

pH  =  log-L  =  log  |^  +  log  9—-^  (13) 

[H+]  Kw  ot 


GENERAL   RELATIONS   AMONG   ACIDS   AND    BASES 


27 


With  the  introduction  of  Kw,  the  dissociation  constant  of  water, 
into  our  equations  it  becomes  advisable  to  consider  its  numerical 
value.  Kw  has  been  determined  in  a  variety  of  ways  of  which 
the  following  are  examples.  Kohlrausch  and  Heydweiller  (1894) 
determined  the  electrical  conductivity  of  extremely  pure  water. 
Assuming  that  the  conductance  is  proportional  to  the  mobility  of 


Fig.  2.  Dissociation  Cueves  and  Dissociation-Residue  Curves 

A.  Dissociation  curve  of  acid,  log  —  =  8.0. 

Ka 

B.  Dissociation  curve  of  acid,  log  —  =  4.8. 

C.  Dissociation-residue  curve  of  acid,  log  —  =  4.8,  or  dissociation  curve 

Ka 

of  a  base  log  —  =  log  — -  —  4.8. 
Kb  Kw 

the  hydrogen  and  the  hydroxyl  ions,  and  that  these  are  present  in 
equal  concentrations,  their  product  is  found  to  be  1.1  X  10~14. 
The  hydrolysis  of  methyl  acetate  having  been  found  to  be  pro- 
portional to  the  concentration  of  hydroxyl  ions,  Wijs  (1893) 
determined    the    hydrolysis    by    water    and    found    Kw  =  1.44 

X  io-14. 

By  determining  the  hydrogen  ion  concentration  with  the 
hydrogen  electrode  in  solutions  of  known  hydroxyl  ion  con- 
centration (as  determined  by  conductance  measurements),  Kw 
is  obtained  from  the  product  of  the  concentrations  of  the  two  ions. 


28 


THE  DETERMINATION  OF  HYDROGEN  IONS 


By  this  method  Lewis,  Brighton  and    Sebastian    (1917)    found 
the  value  1.012  X  10"14  at  25°C. 

Kolthoff  (1921)  has  compiled  the  following  table  showing  the 
dissociation  constant  of  water  at  different  temperatures  as  given 
by  different  authors  and  methods: 


TEMPER- 
ATURE 

i 

ii 

in 

IV 

0° 

0.12  X  10"14 

0.14  X  10~" 

0.089  X  10-" 

18° 

0.59  X  10~14 

0.72  X  10"" 

0.74  X  10~" 

0.46    X  10"" 

25° 

1.04  X  10"" 

1.22  X  10"" 

1.27  X  10"" 

0.82    X  10-" 

50° 

5.66  X  10~" 

8.7    X  10"" 

100° 

58.2    X  10~14 

74.0    X  10~14 

48.0      X  10-" 

I.  Kohlrausch  and  Heydweiller  recalculated  by  Heydweiller  (1909). 

II.  Lorenz  and  Bohi  (1909). 

III.  Michaelis  (1914). 

IV.  Noyes  and  coworkers  (1907). 


The  following  values  of  log  zz~  given  by  Michaelis  (1914)  were 

X\-W 

obtained  on  a  somewhat  different  basis  from  that  used  by  Lewis, 
Brighton  and  Sebastian  (1917). 

Since  in  pure  water  [H+]  =  [OH"],  [H+]  or  [OH~]  =  VKW. 
Hence  from  the  datum  of  Lewis,  Brighton  and  Sebastian  the 
normality  of  H+  or  OH-  in  pure  water  at  25°C.  is  VKW  =  1.006 
X  10~7  (practically  pH  =  7.0). 

In  the  following  pages  wherever  we  have  occasion  for  purposes 
of  illustration  to  use  a  numerical  value  for  Kw  we  shall  employ  the 
rounded  value  10-14. 

Introducing  the  numerical  value  of  Kw  into  equation  (13) 
we  have  the  convenient  form : 


1        ,      (1  —  «) 
pH  =  14  -  log  -=-  +  log  i 1 

Kb  a 


(14) 


In  figure  2  we  have  plotted  a  as  percentage  dissociation.  It  is 
obvious  that  the  percentage  dissociation  residue  will  give  the 
complement  of  the  dissociation  curve  and  will  cross  any  partic- 
ular one  of  these  at  the  fifty  per  cent  dissociation  point.  See,  for 
example,  the  curve  C  of  figure  2. 


GENERAL   RELATIONS   AMONG   ACIDS   AND   BASES 


29 


Now  by  comparing  equation  (10)  with  equation  (14)  it  is  found 
that  the  curve  for  the  dissociation-residue  of  an  acid  is  identical 
with  the  curve  for  the  dissociation  of  a  base  when  Ka  of  the  acid 

is  related  to  Kb  of  the  base  as  log  ^r  =  14  —  log  — .     In  other 


K, 


TABLE  3 


Kb 


TEMPERATURE 

l 

LOGTf— 
KW 

pH  OP  NEUTRAL  POINT 

16 

14.200 

7.10 

17 

14.165 

7.08 

18 

14.130 

7.07 

19 

14.100 

7.05 

20 

14.065 

7.03 

21 

14.030 

7.02 

22 

13.995 

7.00 

23 

13.960 

6.98 

24 

13.925 

6.96 

25 

13.895 

6.95 

26 

13.860 

6.93 

27 

13.825 

6.91 

28 

13.790 

6.90 

29 

13.755 

6.88 

30 

13.725 

6.86 

31 

13.690 

6.85 

32 

13.660 

6.83 

33 

13.630 

6.82 

34 

13.600 

6.80 

35 

13.567 

6.78 

36 

13.535 

•6.77 

37 

13.505 

6.75 

38 

13.475 

6.74 

39 

13.445 

6.72 

40 

13.420 

6.71 

words  curve  C  (fig.  2)  is  either  the  dissociation-residue  curve  of 
an  acid  for  which  log  —  =  4.8  or  the  dissociation  curve  of  a  base 

for  which  log—  =  9.2  (since  14  -  9.2  =  4.8). 

lVb 

The  importance  of  this  relation  lies  in  the  fact  that  a  deter- 
mination of  the  effect  of  hydrogen  ion  concentration  on  some 
process  may  not  reveal  whether  the  phenomenon  has  to  do  with 


30  THE  DETERMINATION  OF  HYDROGEN  IONS 

an  acid  or  a  base,  unless  an  independent  method  reveals  the  nature 
of  the  active  substance. 

The  student  will  find  it  interesting  to  plot  dissociation  curves  for  acids 
with  percentage  dissociation  as  one  coordinate  and  pH  as  the  other,  and 

then  dissociation  curves  for  bases  with  log  .„„_.  (which  may  be  called 

pOH)  as  one  of  the  coordinates  plotted  inversely  as  pH.  At  a  given  temper- 
ature and  given  value  for  Kw  there  is  a  fixed  value  for  pOH  at  each  value 
for  pH.  This  follows  directly  from  equation  (6) ;  and  it  is  particularly  to 
be  noted  that  in  deriving  this  relation  we  need  not  fix  the  position  of  the 
pOH  scale  in  its  relation  to  the  pH  scale  by  confining  our  attention  to  the 
special  case  where  [H+]  =  [OH-],  occurring  roughly  at  pH  7.0.  Indeed  the 
so-called  neutral  point  (pH  7.0)  may  be  considered  only  as  a  convenient, 
mental  reference  point  having  comparatively  little  physical  significance. 
It  is  not  the  point  to  which  titrations  are  led,  except  under  the  rare  con- 
dition that  the  acid  and  the  base  are  of  exactly  equal  strength;  and  it  is 
of  far  less  importance  for  amphoteric  electrolytes  than  is  the  isoelectric 
point  of  the  given  ampholyte. 

Having  plotted  the  two  systems  mentioned  above  the  student  will  find 
it  interesting  to  assume  that  for  moderate  variations  of  temperature  the 
dissociation  constants  of  acids  and  bases  do  not  change  seriously,  and  then 
to  note  the  shift  in  the  two  systems  relative  to  one  another  when  Kw  is 
altered  with  temperature. 

The  treatment  accorded  simple  acids  and  bases  may  be  ex- 
tended to  poly-acidic  acids  and  poly-basic  bases  as  well  as  to 
those  compounds  containing  both  acidic  and  basic  groups  which 
are  called  amphoteric  electrolytes.  It  seems  to  be  true  very  often 
for  such  compounds  that  they  dissociate  in  steps  as  is  illustrated 
in  the  titration  curve  of  the  tri-acidic  phosphoric  acid  shown  on 
page  41.  In  this,  as  in  many  other  cases,  the  several  dissocia- 
tion constants  are  of  such  widely  different  magnitudes  that,  when 
we  plot  the  dissociation  curves  as  if  of  separate  acids  possessing 
these  dissociation  constants,  the  curves  do  not  seriously  overlap. 

Such  acids  may  therefore  be  treated  as  if  composed  of  two  or 
more  independent  acids.  The  effect  produced  when  two  dissocia- 
tion constants  lie  closer  together  is  illustrated  by  the  titration  curve 
of  o-phthalic  acid  shown  on  page  273.  If  in  this  case  the  formal 
dissociation  curve  of  a  simple  acid  be  plotted  over  the  main 
position  of  each  section  of  the  phthalate  curve,  it  will  be  found 
(as  shown  by  Acree)  that  the  experimental  curve  follows  very 
closely  the  interpolated  resultant  of  the  two  formal  single  curves. 


GENERAL   RELATIONS   AMONG   ACIDS   AND    BASES 


31 


For  amphoteric  electrolytes  (i.e.,  electrolytes  containing  acidic 
and  basic  groups)  a  relation  of  great  importance  to  protein  chem- 
istry may  be  illustrated  by  -the  conduct  of  the  simple  ampholyte, 
p-amino  benzoic  acid.  The  acid  dissociation  constant  Ka  is 
6.8  X  10~6  and  the  basic  dissociation  constant  Kbis  2.3  X  10-12 
(Scudder).  Translating  these  into  the  corresponding  pH  values 
we  have  5.17  and  2.36.  If  we  regard  the  compound  as  if  it  were 
made  up  of  an  acid  and  a  base  with  the  above  dissociation  con- 


Fig.  3.  Dissociation  and  Dissociation-Residue  Curves  op  p-Amino- 

benzoic  Acid 
Treated  as  if  the  amphoteric  electrolyte  were  composed  of  an  acid  of 

log  —  =  5.17  and  a  base  of  log  —  =  log  — —  —  2.36. 
Ka  Kb  Kw 


stants  (in  terms  of  pH)  and  each  independent  of  the  other,  we 
can  plot  the  dissociation  curves  of  each  with  the  aid  of  equations 
(10  and  14).  In  each  case  the  dissociation-residue  curves  are  the 
complements.  These  are  plotted  in  figure  3  with  heavy  lines. 
It  is  seen  that  they  cross  at  pH  =  3.77.  This  means  that  at 
pH  =  3.77  there  is  a  maximum  of  undissociated  residue.  Now 
if  the  salts  are  more  soluble  than  the  free  compound  itself  there 
should  be  a  minimum  solubility  at  pH  3.77.  Michaelis  and  David- 
sohn  (1910)  found  a  minimum  solubility  at  pH  3.80. 

Turning  again  to  the  light  lines  A  and  B  of  figure  3,  we  see  that 
their  intersection  is  at  a  point  where  the  percentage  of  the  com- 


32  THE   DETERMINATION   OF   HYDROGEN   IONS 

pound  ionized  as  an  anion  is  equal  to  the  percentage  ionized  as 
a  cation.  In  other  words  the  amount  carrying  a  negative  charge 
is  equal  to  the  amount  carrying  a  positive  charge.  Because  of 
this  equality  the  point  where  it  occurs  is  called  the  isoelectric 
point. 

If  we  still  maintain  the  simple  conditions  postulated  in  this 
elementary  treatment,  we  can  calculate  the  isoelectric  point  from 
the  dissociation  constants  of  an  amphoteric  electrolyte. 

Consider  an  amphoteric  electrolyte  of  the  type  HROH  for 
which  we  have  the  following  equilibrium  equations: 

[HR+]  [OH- 


[HROH] 
[ROB]  [H+] 


=  Kb  (15) 

-  Ka  (16) 


[HROH] 

When  [HR+]  =  [ROH]  (isoelectric  condition) 

[HROH]  _        [HROH] 
b    [OH-]    "      a      [H+] 

Hence  [H+]  -  W— K  (17) 

"Kb 

In  the  case  cited  above  [H+]  =  W  '^  — •— ;      10-14 


2.3  X10-12 


or  pH  =  log  ^—  =  3.77 

P  *  [H+ 


Furthermore  from  equations  (15)  and  (16) 

[HR+]  +  [ROH-]  -  Kb  [HROHHH3  +        [HROH] 

Kw  lH+] 

If  we  let  [HR+]  +  [ROH-]  =  X,  X  becomes  a  minimum  when 


0,  a  condition  fulfilled  when  [H+]  =  J^  K, 


d  [H+]        '  L      J        IK 

In  other  words  the  sum  of  the  anion  and  cation  concentrations 
is  a  minimum  at  the  isoelectric  point. 

Only  in  case  Ka  =  Kb  will  the  isoelectric  point  correspond  with 
the  "neutral  point." 


GENERAL   RELATIONS    AMONG   ACIDS    AND    BASES  33 

It  is  at  once  evident  that  the  isoelectric  point  of  an  amphoteric 
electrolyte  is  a  point  at  or  near  which  there  should  tend  to  occur 
maximal  or  minimal  properties  of  its  solution.  Indeed  at  such 
points  have  been  found  to  occur  minimum  solubilities,  minimum 
viscosities,  minimum  swelling,  optimum  agglutinations,  etc. 

It  should  be  emphasized  that  the  foregoing  relationships  have 
been  developed  from  very  simple  conditions.  When  these  con- 
ditions have  been  approached  experimental  verification  has  been 
found.  The  insight  thus  gained  has  led  to  a  better  understanding 
of  complex  ampholytes,  the  complete  equilibria  of  which  can 
be  seen  only  in  broad  outline.  In  attempting  to  formulate 
more  precisely  the  equilibrium  equations  which  hold  under  more 
complex  conditions  than  those  postulated  above,  Michaelis  (1920) 
has  started  with  the  influence  of  uni-univalent  salts  upon  a  simple 
ampholyte  and  has  then  extended  his  propositions  to  cover  the 
influence  of  divalent  ions  and  the  influence  of  micelle  formation. 
It  is  of  special  interest  to  note  that  he  can  account  for  the  dis- 
placement of  the  precipitation  optimum  from  the  isoelectric 
point  by  the  influence  of  salts  and  that  he  finds  it  necessary  to 
caution  against  considering  the  isoelectric  point  to  be  always 
identical  with  the  point  of  maximum  dissociation  residue.  He 
also  outlines  the  direction  in  which  various  relations  will  be 
modified  by  the  aggregation  of  the  undissociated  ampholyte 
into  micelles. 

SUPPLEMENTARY  REFERENCES 

Texts  on  the  principles  of  electrolytic  dissociation :  LeBlanc,  Jones,  Nernst, 

Ostwald,  Stieglitz  (1917). 
Generalized  relations  among  acids  and  bases:  Henderson  (1908),  Michaelis 

(1914,  1922),  S0rensen  (1912). 


CHAPTER  II 

Some  Special  Aspects  of  Acid-Base  Equilibria 

Words  are  the  footsteps  of  reason. — Francis  Bacon. 

In  the  foregoing  chapter  we  have  outlined  the  chief  aspects  of 
acid-base  equilibria.  We  now  have  to  discuss  in  more  detail 
some  of  the  terminology  of  special  use  in  acid-base  studies  and 
also  certain  important  matters  which  are  continually  met  in 
dealing  with  that  class  of  electrolytes  called  the  "strongly  dis- 
sociating" acids,  bases  and  salts. 

THE    pH    SCALE 

v  When  "acidity"  was  resolved  into  its  two  components  the  nor- 
mality unit  was  retained  for  each.  As  a  normal  solution  of  an 
acid  had  been  defined  as  one  containing  in  1  litre  of  solution  the 
equivalent  of  1  gram  atom  of  acidic  hydrogen,  so  the  normal  solu- 
tion of  the  hydrogen  ion  was  defined  to  be  one  containing  in  1 
litre  of  solution  1  gram  atom  of  hydrogen  ions.1 

To  distinguish  between  these  two  components  with  their  com- 
mon unit  it  has  been  suggested  that  we  call  "normality"  in  its 
older  sense  the  quantity  factor  of  "acidity"  and  the  hydrogen  ion 
concentration  the  intensity  factor.  This  may  serve  to  emphasize 
a  distinction,  but  the  suggested  analogy  with  the  quantity  and 
intensity  factors  of  energy  is  confusing  when  we  retain  for  each 
a  unit  of  the  same  category.  Nevertheless  the  two  components 
remain  in  a  restricted  sense  the  quantity  and  intensity  factors  of 
"acidity."  The  one  is  the  total  quantity  of  available  acid.  The 
second,  the  concentration  of  the  hydrogen  ions,  represents  the 
real  intensity  of  "acidity"  whenever  it  is  the  hydrogen  ion  which 
is  the  more  directly  active  participant  in  a  reaction.  This  is 
admirably  expressed  when  we  use  for  hydrogen  ion  concentrations 
a  mode  of  expression  which  links  it  with  the  potential  of  a  hydro- 
gen electrode.     It  so  happens  that  in  determining  the  hydrogen 

1  It  makes  little  difference  whether  the  atomic  weight  of  hydrogen  be 
taken  as  1.008  or  as  1.0  in  calculating  [H+]. 

34- 


SPECIAL   ASPECTS   OF   ACID-BASE    EQUILIBRIA  35 

ion  concentration  with  the  hydrogen  electrode  the  potentials  of 
this  electrode  are  put  into  an  equation  which  reduces  to  the 
form : 

Potential  ,         1 

=  log 


log  frr+i tne  symbol  PH+ 


Numerical  factor  [H+l 

Thus  log  r7jqT  is  at  once  obtained  by  the  most  simple  of  calcula- 
tions. S0rensen  (1909)  saw  that  this  value  serves  to  define  a 
hydrogen  ion  concentration  quite  as  well  as  [H+]  itself  and  in  his 
Enzyme  Studies' II,  he  used  this  mode  of  expression  and  gave  to 

[H- 

As  a  matter  of  typographical  convenience2  we  shall  adopt  pH 
in  place  of  PH+.  Since  this  is  coming  into  wide  usage  its  uniform 
adoption  is  recommended  in  place  of  the  bothersome  variations3 
which  have  made  their  way  into  the  literature. 

Although  S0rensen  has  not  revealed  the  considerations  which 
led  to  the  choice  of  the  letter  P  in  his  symbol,  we  might  regard  P 
as  suggesting  the  potential  (intensity)  factor  of  acidity  in  the 
sense  described  above. 

Writing  the  potential  equation  given  on  page  154  as 

W  =  EF  =  RTln  =tj 
*At*.  [H+] 

it  will  be  seen  thatuE  is  the  intensity  factor  in  the  work  required 
to  carry  a  gram  atom  of  hydrogen  ions  from  concentration  [H+] 
to  concentration  1  normal;  and  pH  is  a  linear  function  of  E. 

pH  is  sometimes  called  the  S0rensen  value  or  S0rensen  unit 
and  following  S0rensen's  original  suggestion  it  is  named  the 
hydrogen  ion  exponent.  The  last  mentioned  name  must  be  used 
with  some  caution  because  of  a  difference  in  sign  between  a 
given  pH  value  and  the  exponent  occuring  when  the  normality 
of  the  corresponding  hydrogen  ion  concentration  is  written.     For 

2  As  is  the  custom  of  the  Journal  of  Biological  Chemistry. 
J      3  Certain  punctilious  authors  have   insisted   that   the  original  symbol 
should  be  retained  but  have  made  the  mistake  of  assuming  it  to  be  PH- 
The  following  variations  are  found  in  the  literature: 

ph,pH,Ph,PH,Ph,PH,Ph,PH,  also  each  case  italicised. 


36  THE   DETERMINATION   OF   HYDROGEN   IONS 

examples  —  7  is  the  exponent  in  10-7,  but  the  pH  value  correspond- 
ing to  [H+]  =  10-7n  is  +7. 

The  convenience  of  pH  over  [H+]  is  manifest  when  we  compare 
the  numerical  values  encountered  in  chemical  and  physiological 
studies.  For  instance,  one  enzyme  may  operate  most  actively  at 
a  hydrogen  ion  concentration  of  0.01  normal  while  another  is 
most  active  at  0.000,000,001  normal.  While  convenient  abbre- 
viations of  such  unwieldy  values  are  1  X  10~3  and  1  X  10~9, 
there  remains  the  difficulty  of  plotting  such  values  on  ordinary 
cross-section  paper.  If  the  difference  between  0.000,000,001  and 
0.000,000,002  is  given  a  length  of  one  millimeter,  the  difference 
0.01  to  0.02  when  plotted  on  the  same  scale  would  be  ten  kilo- 
meters, ten  kilometers  distant.  Evidently  the  logarithmic 
spacing  should  be  followed  and  fortunately  it  is  the  log- 
arithmic plotting  of  hydrogen  ion  concentration  (in  terms  of 
pH)  which  correctly  depicts  the  fact  that  the  difference  between 
1  x  10-9  and  2  x  10-9  may  be  as  important  for  one  set  of 
equilibria  as  the  enormously  greater  difference  between  1  X  10_J 
and  2  X  10-2  is  for  another  set  of  equilibria.  This  is  revealed 
in  the  charts  on  previous  and  subsequent  pages. 

Thus  both  convenience  and  the  nature  of  the  physical  facts 
compel  us  directly  or  indirectly  to  operate  with  some  logarithmic 
function  of  [H+]. 

It  is  unfortunate  that  a  mode  of  expression  so  well  adapted  to  the  treat- 
ment of  various  relations  should  conflict  with  a  mental  habit.  [H+]  repre- 
sents the  hydrogen  ion  concentration,  the  quantity  usually  thought  of  in 
conversation  when  we  speak  of  increases  or  decreases  in  acidity.  pH  varies 
inversely  as  [H+].    This  is  confusing. 

The  normality  mode  of  expression  has  historical  priority  and  conse- 
quently conventional  force.  Since  there  is  a  hydrogen  ion  concentration 
for  each  hydroxyl  ion  concentration  it  became  the  custom,  following  Fried- 
enthal  (1904),  to  express  both  acidities  and  alkalinities  in  terms  of  [H+], 
This  gave  a  scale  of  one  denomination  and  the  meaning  of  "higher"  and 
of  "lower"  became  firmly  fixed.  Now  we  meet  the  new  scale  with  its  direc- 
tion reversed.  The  inconvenience  is  unquestionable  and  very  largely  be- 
cause of  it  the  pH  scale  has  been  criticized. 

See  the  discussion  in  the  Journal  of  the  Washington  Academy  of  Sciences 
by  Wherry  and  Adams  (1921)  and  by  Clark  (1921).  Wherry's  (1919)  chief 
object  is  to  establish  a  scale  of  convenient  direction  but  in  doing  so  he 
gains  a  superficial  advantage  at  the  expense  of  several  simple  and  very 
important  experimental  and  theoretical  relations  which  he  has  not  taken 
into  consideration. 


SPECIAL   ASPECTS   OF   ACID-BASE   EQUILIBRIA 


37 


In  Chapter  XIX  there  will  be  advanced  a  reason  for  adhering 
to  the  use  of  the  pH  introduced  by  S0rensen;  but  at  this  point  it 
may  be  well  to  say  that  in  both  of  the  two  chief  methods  of  deter- 
mining hydrogen  ion  concentration  we  encounter  physical  rela- 
tions which  make  the  errors  proportional  to  pH  rather  than 
to  [H+].  Furthermore,  pH  is  the  more  directly  related  to  certain 
electrode  phenomena  which  are  partially  dependent  upon  hydro- 
gen ion  concentration  and  therefore  pH  is  useful  in  dealing  with 
subjects  outside  the  strict  limits  of  hydrogen  electrode 
measurements. 

The  gross  relation  of  [H+]  to  pH  is  shown  in  the  following  table. 
See  also  table  B  appendix. 


/     r 


[H+] 

pH 

[H+] 

pH 

io-° 

0 

lO"8 

8 

lO"1 

1 

10"9 

9 

10"2 

2 

10-io 

10 

io-» 

3 

10"11 

11 

io-« 

4 

10"12 

12 

io-« 

5 

10~13 

13 

io-« 

6 

10~14 

14 

10"T 

7 

The  following  symbols  indicating  hydrogen  ion  concentration 


in  normality  are  encountered  in  the  literature  [H+];  [H' 

CH;h. 


jn 


s. 


THE    EFFECT    OF   DILUTION 


A  litre  of  normal  acid  becomes  a  fifth  normal  solution  if  diluted 
to  5  litres;  the  hydrogen  ion  concentration  may  in  many  instances 
be  affected  too  little  for  the  change  to  be  detected  by  any  but 
refined  methods.  This  apparent  anomaly  is  frequently  encoun- 
tered and  sometimes  advantage  of  it  is  taken  in  the  dilution  of 
solutions  otherwise  too  dense  optically  for  the  application  of  the 
indicator  method.  The  effect  of  dilution  upon  the  hydrogen  ion 
concentration  of  a  solution  may  be  briefly  generalized  by  some 
approximations. 


38  THE   DETERMINATION   OF   HYDROGEN   IONS 

Consider  an  acid  of  the  type  HA  for  the  dissociation  of  which 
we  have  the  equilibrium  equation: 

[H+]  X  [A~]  _ 
[HA] 

If  Ka  is  small  there  must  obviously  be  a  large  reserve  of  undis- 
sociated  acid  so  long  as  the  concentration  of  total  acid  is  high. 
As  the  solution  is  diluted  this  reserve  dissociates  to  keep  Ka 
constant;  but  there  is  a  readjustment  of  all  components  which 
can  be  conveniently  followed  only  by  means  of  the  simple  algebraic 
equation  expressing  the  equilibrium  condition. 

If  the  acid  alone  is  present  in  the  solution  we  may  assume  that 
[Ai  =  [H+].     Also  if  Sa  =  the  total  acid,  [HA]  =  Sa  -  [H+]. 

Substituting  these  in  the  above  equation  and  solving  for  [H+] 
we  have: 

[H+]  =  WKaSa  +  ^--Ka  (18) 

*  4        2 

When  Ka  is  small  in  relation  to  S  a 

[H+]  S  VkK  (19) 

Compare  the  equation  on  page  19.  On  these  assumptions  the 
hydrogen  ion  concentration  should  vary  with  dilution  of  the 
solution  (diminution  of  Sa)  only  as  the  square  root  of  KaSa. 

If  there  is  present  a  salt  of  the  acid  we  can  apply  the  equation 
derived  on  page  24  which  shows  that  the  hydrogen  ion  concen- 
tration of  a  mixture  of  a  weak  acid  and  its  highly  dissociated  salt 
is  determined  approximately  by  the  ratio  of  acid  to  salt.  Since 
dilution  does  not  change  the  ratio,  such  a  mixture  should  not  suf- 
fer a  change  of  hydrogen  ion  concentration  beyond  the  narrow 
limits  set  by  the  approximate  treatment  with  which  this  relation 
was  derived. 

Therefore,  except  for  solutions  of  high  hydrogen  ion  concentra- 
tion induced  by  the  presence  of  unneutralized  strong  acids,  the 
hydrogen  ion  concentration  should  vary  with  dilution  somewhere 
between  the  zero  change  indicated  by  the  last  approximation  and 
the  square  root  relation  first  indicated. 

Such  a  conclusion  takes  no  account  of  changes  of  equilibrium 
which  sometimes  occur  in  colloidal  solutions. 


SPECIAL   ASPECTS    OF   ACID-BASE    EQUILIBRIA 


39 


For  bases  and  amphoteric  electrolytes  similar  relations  may  be 
deduced.     One  <jr  two  actual  cases  may  be  of  interest. 

S0rensen  has  given  the  following  table  of  the  pH  values  of  dif- 
ferent dilutions  of  asparagine  and  glycocoll. 


MOLECULAR  CONCEN- 
TRATION OF  GLY- 
COCOLL 

pH 

MOLECULAR  CONCEN- 
TRATION OF  ASPAR- 
AGINE 

pH 

1.0 

6.089 

1.0 

2.954 

0.1 

6.096 

0.1 

2.973 

0.01 

6.155 

0.01 

3.110 

0.001 

6.413 

0.001 

3.521 

0.0001 

6.782 

0.0001 

4.166 

The  dilution  he're  is  ten-fold  at  each  step,  yet  the  increase  in 
pH  is  very  small  while  the  solutions  are  beween  1.0-0.01  M. 

Walpole  (1914)  besides  giving  data  on  the  hydrogen  electrode 
potentials  of  various  dilutions  of  acetic  acid  and  "standard  ace- 
tate," has  determined  the  effect  of  a  twenty-fold  dilution  of 
various  acetic  acid-sodium  acetate  mixtures.  The  change  of  pH 
on  twenty-fold  dilution  of  standard  acetate  is  about  0.08  pH; 
and  of  mixtures  of  acetic  acid  and  sodium  acetate  which  He  on 
the  flat  part  of  the  curve  the  change  of  pH  is  of  the  same  order 

acetic  acid 

of  magnitude.    When  the  ratio — - -—reaches   19/1    the 

sodium  acetate 

change  is  about  0.3  pH. 


BUFFER  ACTION 

If  we  were  to  add  to  1  liter  of  perfectly  pure  water  of  pH  7.0, 
1  cc.  of  0.01n  HC1,  the  resulting  solution  would  be  about  pH 
5.0  and  very  toxic  to  many  bacteria.  If,  on  the  other  hand,  we 
were  to  add  this  same  amount  of  acid  to  a  liter  of  a  standard  beef 
infusion  medium  of  pH  7.0,  the  resulting  change  in  pH  would 
be  hardly  appreciable.  This  power  of  certain  solutions  to  resist 
change  in  reaction  was  commented  upon  by  Fernbach  and  Hubert 
(1900)  who  likened  the  resistance  of  phosphate  solutions  to  a 
"tampon."  The  word  was  adopted  by  S0rensen  (1909)  and  in 
the  German  rendition  of  his  paper  it  became  " Puffer"  and  thence 
the  English  "buffer."     There  has  been  some  objection  to  this 


40  THE   DETERMINATION   OF   HYDROGEN   IONS 

word  so  applied  but  it  now  possesses  a  clear  technical  meaning  and 
I  is  generally  used.  By  buffer  action  we  mean  t£e  resistance  ex- 
hibited by  a  solution  to  change  in  pH  through  the  addition  or  loss 
of  acid  or  alkali.  This  may  be  illustrated  by  titration  curves  such 
as  those  shown  in  figures  4,  5  and  6.  The  construction  of  such 
curves  may  be  illustrated  by  the  following  example. 

A  1  per  cent  solution  of  Witte  peptone  was  found  to  have  a 
pH  value  of  6.87.  To  equal  portions  of  the  solution  were  added 
successively  increasing  amounts  of  O.In  lactic  acid  and  the  result- 
ing pH  was  measured  in  each  case.  There  were  also  added  to 
equal  portions  of  the  solution  successively  increasing  amounts  of 
O.In  NaOH  and  the  resulting  pH  was  measured  in  each  case. 
The  pH  values  were  then  plotted  on  cross  section  paper  as  ordi- 
nates  against  the  amount  of  acid  or  alkali  added  in  each  case  as 
abscissas.  This  gave  curve  1  shown  in  figure  4.  The  other 
curve  shown  in  this  figure  was  constructed  with  data  obtained 
with  a  5  per  cent  solution  of  Witte  peptone.  The  curves  of  fig- 
ures 5  and  6  were  obtained  in  a  similar  way. 

These  curves  illustrate  the  following  points. 
'  Figure  4  shows  that  the  buffer  action  of  a  solution  is  dependent 
upon  the  concentration  of  the  constituents.  The  5  per  cent  solu- 
tion is  much  more  resistant  to  change  in  pH  than  the  1  per  cent 
solution.  It  will  also  be  noticed  that  in  either  case  the  buffer 
action  is  not  the  same  at  all  points  in  the  curve.  In  other  words 
the  buffer  action  can  not  be  expressed  by  a  constant  but  must 
be  determined  for  each  region  of  pH.  This  is  illustrated  even 
more  clearly  by  the  titration  curve  for  phosphoric  acid  (fig.  5). 
At  the  point  where  the  solution  contains  only  tha:primary  phos- 
phate and  again  where  it  contains  only  the  secondary  phosphate 
there  is  very  little  buffer  effect  indeed. 

Furthermore  the  buffer  action  of  a  solution  may  not  be  due 
entirely  to  the  nature  of  the  constituents  titrated  but  also  to.  the 
nature  of  the  substance  with  which  it  is  titrated.  This  point 
may  be  illustrated  by  titrating  a  beef  infusion  medium  in  the  one 
case  with  hydrochloric  acid  and  in  the  other  case  with  lactic  acid, 
both  of  the  same  normality  (see  fig.  6).  It  will  be  seen  that  at 
first  the  two  curves  are  identical.  As  the  region  is  approached 
where  the  dissociation  of  the  "weak"  lactic  acid  is  itself  sup- 
pressed because  of  the  accumulation  of  lactate  ions  and  the  high 


SPECIAL   ASPECTS   OF  ACID-BASE   EQUILIBRIA 


41 


A 

^ 

■  5 

•7 

e 

/ 

<*/ 

O 

/ 

T 

k 

% 

r 

/ 

r» 

X 

/ 

j 

/ 

A 

2 

> 

c 

) 

r 

\ 

4 

c.c. 

Fig.  4.  Titration  Curves  of  1  Per  Cent  and  5  Per  Cent  Peptone 

Ten  cubic  centimeters  of  peptone  solution  titrated  with  N/10  lactic  acid 
(to  right)  and  with  N/10  NaOH  (to  left). 


i!£5 

4 

\ 

' 

foyi 

Si 

V 

6 

10 
PH 

KjHP 

\ 

V 

W 

c.c. 


50 


100 


150 


Fig.  5.  Titration  Curve  of  Phosphoric  Acid 
Fifty  cubic  centimeters  M/10  H3P04  titrated  with  N/10  KOH. 


42 


THE   DETERMINATION   OF   HYDROGEN   IONS 


concentration  of  the  hydrogen  ions,  further  addition  of  this  acid 
has  comparatively  little  effect.  The  strong  hydrochloric  acid 
on  the  other  hand  continues  to  be  effective  until  its  dissociation, 
too,  at  very  high  hydrogen  ion  concentrations  is  suppressed. 


PH 


8 


f> 

LA 

cue. 

c.c. 


20 


40 


60 


Fig.  6.  Titration  Curves  op  a  Beep  Infusion  Medium 

One  hundred  cubic  centimeters  medium  titrated  with  N/5  HC1  and  with 
N/5  lactic  acid. 

These  examples  will  suffice  to  make  it  evident  that  the  buffer 
action  of  a  solution  is  dependent  upon  the  nature  and  the  concen- 
tration of  the  constituents,  upon  the  pH  region  where  the  buffer 
action  is  measured  and  upon  the  nature  of  the  acid  or  alkali 
added.  To  connect  all  these  variables  is  a  difficult  problem. 
Koppel  and  Spiro  (1914)  have  attempted  to  do  so  but  they  have 
necessarily  had  to  leave  out  of  consideration  another  factor.     If 


SPECIAL  ASPECTS   OF  ACID-BASE   EQUILIBRIA  43 

there  are  present  any  bodies  which  tend  to  adsorb  any  of  the  con- 
stituents of  a  solution  which  can  affect  the  hydrogen  ion  concen- 
tration of  a  solution,  these  bodies  will  tend  to  act  as  buffers  or 
will  affect  the  buffer  action  of  the  solution.  Henderson  (1909)  has 
called  attention  to  this  and  Bovie  (1915)  has  shown  in  a  very 
interesting  way  the  buffer  action  of  charcoal.  Since  some  culture 
media  or  cultures  and  many  of  the  solutions  whose  buffer  action 
must  be  studied  for  physiological  purposes,  contain  undissolved  or 
colloidal  material  which  may  act  in  this  way,  it  seems  best  to 
consider  buffer  action  in  its  broadest  sense,  and  to  express  it  by 
the  relative  slopes  of  titration  curves  determined  experimentally. 
Further  illustrations  of  titration  curves  of  culture  media  will  be 
found  in  the  papers  of  Clark  (1915)  and  of  Bovie  (1915).  Titra- 
tion curves  of  some  inorganic  solutions  will  be  found  in  a  paper 
by  Hildebrand  (1913). 

The  reader  will  have  perceived  the  elementary  theory  under- 
lying buffer  action.  The  titration  curve  of  phosphoric  acid  (fig.  5) 
illustrates  the  principles  discussed  on  previous  pages.  The  titra- 
tion curve  of  a  "peptone"  solution  integrates  as  it  were  the  effects 
of  acids,  bases  and  ampholytes,  in  complex  mixture. 

Returning  to  figure  1  we  see  that  along  the  flat  portion  of  the 
curve  considerable  alkali  has  to  be  added  to  produce  much  change 
in  pH.  Conversely,  the  addition  of  a  strong  acid  would  not  have 
anywhere  near  the  effect  at  this  flat  portion  of  the  curve  that  it 
would  have  near  either  end.  Thus  it  is  evident  that  a  mixture  of 
a  single  acid  and  its  salt  will  tend  to  stablize  the  pH  of  the  solution 
only  within  a  certain  narrow  zone  having  vague  boundaries. 
Mixtures  buffering  the  solution  within  such  a  pH  zone  are  often 
referred  to  as  "regulator  mixtures."  They  are  of  very  great 
value  to  the  analyst  and  the  physiological  chemist  in  that  they 
furnish  a  means  of  stablizing  the  hydrogen  ion  concentration 
within  a  predetermined  zone.  The  middle  point  of  this  zone, 
where  the  strongest  buffer  action  is  exerted,  is  determined  approxi- 
mately as  shown  on  page  25  by  the  dissociation  constant  of  the 
acid  or  base  concerned.  Other  things  being  equal  the  choice  of 
mixtures  is  thus  revealed  in  a  table  of  dissociation  constants. 
*  [  More  theoretical  treatments  of  the  subject  are  given  in  the 
papers  of  Henderson  (1909),  S0rensen  (1909),  S0rensen  (1912), 
Michaelis  (1914)  and  Koppel  and  Spiro  (1914). 


44  THE   DETERMINATION   OF   HYDROGEN   IONS 

Unless  a  solution  is  buffered  to  some  extent  in  some  way,  it  is 
almost  impossible  to  make  an  accurate  electrometric  determina- 
tion of  the  pH;  and  because  of  the  influence  of  traces  of  carbon 
dioxid  and  other  acidic  or  basic  contaminations  such  solutions 
may  be  very  unsuitable  when  used  for  physiological  purposes. 
Thus  the  failure  to  buffer  against  the  effect  of  so-called  neutral 
salts  which  are  not  truly  neutral  may  lead  to  gross  error.  In  like 
manner  the  failure  to  buffer  has  rendered  physiologically  unstable 
certain  so-called  synthetic  and  supposedly  stable  culture  media. 

In  the  preparation  of  standard  buffer  mixtures  it  is  of  course,  preferable 
to  use  a  high  grade  of  water  if  accuracy  is  required  but  there  is  little  need 
of  carrying  this  to  an  extreme.  "Conductivity  water"  is  sometimes  speci- 
fied for  the  preparation  of  special  standards  because  the  ordinary  distilled 
water  of  certain  regions  of  the  country  is  such  that  "distilled  water"  means 
nothing.    The  exercise  of  judgment  is  advantageous. 

The  maintenance  of  "neutrality"  by  such  solid  reagents  as  calcium  car- 
bonate may  be  considered  as  a  buffer  action.  It  is  very  important  to  note 
however  that  the  use  of  calcium  carbonate  may  become  a  grossly  inefficient 
procedure.  To  show  its  inefficiency  the  author  has  placed  at  the  bottom  of 
a  test  tube  a  deep  layer  of  very  finely  divided,  freshly  precipitated  and  well 
washed  calcium  carbonate  and  overlaid  this  with  cultures  of  bacteria  and 
molds  in  sugar  media.  Indicators  show  that  unless  the  calcium  carbonate 
is  frequently  and  thoroughly  shaken  with  the  medium  only  the  solution 
in  direct  contact  with  the  calcium  carbonate  is  neutralized.  Molds  may 
develop  an  acidity  as  high  as  pH  2  within  a  few  millimeters  of  the  carbonate. 

THE    CONDUCT   OF   STRONG   ELECTROLYTES 

The  relations  set  forth  in  the  preceding  pages,  even  in  the 
approximate  form  adopted  to  keep  the  distinctive  lines  of  the 
picture  clear,  afford  in  their  experimental  verification  the  best  of 
evidence  that  the  theory  of  electrolytic  dissociation  is  essentially 
correct.  That  it  is  incomplete  is  shown  when  we  turn  to  the 
examination  of  the  quantitative  data  for  strong  electrolytes — 
acids  such  as  hydrochloric  and  nitric  and  salts  such  as  the  simple 
chlorides.  For  instance,  if  the  conductance  of  a  solution  is 
ascribed  to  the  concentration  and  the  mobilities  of  the  ions,  and 
if  the  mobilities  be  considered  constant  at  all  dilutions,  the  con- 
ductance data  should  satisfy  the  Ostwald  dilution  law  and  furnish 

a  dissociation  constant.    The  Ostwald  dilution  law  is  q  _  a)v  =  * 


SPECIAL   ASPECTS   OF   ACID-BASE    EQUILIBRIA  45 

where  a  is  the  degree  of  dissociation,  v  the  dilution  and  k  the 
equilibrium  constant  which  should  be  independent  of  the  dilution; 
a  should  be  equal  to  the  ratio  of  equivalent  conductance  at  dilu- 
tion v  to  equivalent  conductance  calculated  for  infinite  dilution. 
For  potassium  chloride,  k  varies  from  0.049  at  1000  dilution  to 
0.541  at  10  dilution.  The  discrepancies  with  hydrochloric  acid 
are  comparable. 

The  reader  will  recall  that  in  the  derivation  of  the  equilibrium 
constant  (page  19)  there  was  introduced  an  assumption  full  of 
danger.  The  assumption  was  that  the  physical  environment, 
within  which  occur  the  reactions  of  dissociation  and  recombination, 
remain  constant.  It  has  already  been  mentioned  that  a  change 
in  temperature  changes  the  equilibrium  constant  and  that  a 
change  in  solvent  produces  a  more  profound  effect.  Now  it  is 
not  at  all  improbable  that  the  presence  of  relatively  large  concen- 
trations of  ions  and  especially  of  the  hydrogen  or  hydroxyl  ions 
constitutes  an  environment  appreciably  different  from  that  of  a 
dilute  solution.  If  so,  we  should  hardly  expect  to  find  an  equilib- 
rium constant  holding  over  a  great  range  of  concentration.  Yet 
it  is  by  changing  concentration  that  we  expect  to  so  alter  the 
distribution  of  "species"  that  we  may  demonstrate  the  "mass" 
law  experimentally. 

But  there  are  other  possible  difficulties.  For  instance,  data 
upon  what  may  be  called  the  structure  of  solutions,  the  mutual 
influence  of  solvent  and  solute  upon  association  of  solvent  mole- 
cules, association  of  solute  molecules  and  association  of  solvent 
with  solute  are  still  hazy.  Furthermore  it  is  difficult  to  say 
what  degree  of  separation  constitutes  ionization  as  measured  by 
different  methods.  Therefore  it  is  impossible  to  give  rigidly 
accurate  values  to  the  concentrations  of  active  molecules.  When, 
therefore,  it  is  stated  that  the  anomalies  of  strong  electrolytes 
"disprove  the  mass  law,"  it  may  be  only  a  clumsy  way  of  saying 
that  we  do  not  know  how  to  give  the  case  an  adequate  test. 

To  give  any  adequate  review  of  the  present  status  of  the  prob- 
lem would  require  undue  space  A  most  valuable  review  ap- 
peared in  the  discussions  which  took  place  in  the  Faraday  Society 
and  which  are  published  in  the  December,  1919,  number  of  the 
Transactions.  It  is  there  made  very  evident  that  the  "  anomalies  " 
of  strong  electrolytes  have  been  the  bugbear  of  students  of  ioni- 


46  THE  DETERMINATION  OP  HYDROGEN  IONS 

zation,  have  stimulated  most  brilliant  researches  and  promise  to 
be  the  starting  point  for  new  developments  which  will  harmonize 
the  entire  body  of  data. 

There  have  been  attempts  to  formulate  the  facts  by  means  of 
purely  empirical  equations;  and  then  again  the  pendulum  has 
swung  back  to  a  faith  that  the  original  simple  assumptions  could 
be  satisfied  if  interfering  factors  were  discovered  and  their  numeri- 
cal magnitudes  introduced  as  corrections.  More  recently  there  has 
come  to  the  fore  the  "activity"  concept  of  Lewis.  This  will  be 
mentioned  again  in  Chapter  XIX.  This  concept  has  attained  con- 
siderable success  in  systematizing  the  data;  but  whether  it  will 
have  an  appeal  universal  enough  to  satisfy  minds  of  the  type  of 
Lord  Kelvin,  which  reason  not  only  in  abstract  terms  but  also 
demand  concrete  models,  remains  to  be  seen. 

When  there  occur  in  the  development  of  a  science  such  baffling 
difficulties  as  have  arisen  in  the  case  of  "strong  electrolytes," 
it  is  highly  desirable  to  abandon  both  complex  reasoning  and  end- 
less corrections,  if  an  entirely  new  basis  can  be  found.  This 
statement  will  appear  gratuitous  or  even  foolish  to  those  who  are 
so  possessed  with  the  idea  of  the  complexity  of  aqueous  solutions 
that  they  admit  no  theory  as  sufficient  that  is  not  itself  complex; 
but  the  history  of  other  developments  has  shown  that  in  the  face 
of  similar  complexities  a  simple  basis  of  reference  has  been  found 
and  has  won  acceptance  through  its  convenience. 

Whatever  may  be  the  opinion  of  the  reader  he  will  doubtless 
agree  that  we  are  in  the  midst  of  or  at  the  beginning  of  a  period 
of  transition,  and  that  it  is  incumbent  upon  the  experimenter  to 
keep  his  data  as  free  as  is  convenient  from  confusions  introduced 
by  tacit  assumptions.  In  the  following  treatment  of  our  subject 
assumptions  common  to  the  age  will  remain,  but  at  least  they  will 
be  more  clearly  recognized  than  if  we  straddled  the  issue  that  has 
arisen.  We  shall  therefore  proceed  with  the  concept  of  "con- 
centration" as  commonly  used,  since  it  is  the  more  convenient 
for  elementary  descriptive  text.  Finally  in  Chapter  XIX  we  shall 
redefine  certain  standards  in  such  a  way  as  to  embody  current 
procedures  and  at  the  same  time  relieve  the  biochemist  from 
embarrassments  due  to  the  present  state  of  flux. 

Although  free  acidities  of  a  magnitude  that  fall  within  the 
grosser  uncertainties  of  our  knowledge  of  strong  electrolytes  are 


SPECIAL   ASPECTS    OF   ACID-BASE   EQUILIBRIA  47 

seldom  met  in  physiological  solutions,  the  whole  system  of  pH 
measurements  is  scaled  from  certain  assumptions  regarding  the 
now  uncertain  conduct  of  HC1  as  will  be  shown  in  Chapter  XIX. 
Furthermore  we  have  continually  to  deal  with  solutions  contain- 
ing salts  whose  conduct  is  so  little  understood  that  precise  treat- 
ment is  impossible.  This  will  appear  in  the  so-called  salt  error  of 
indicators  and  the  strange  fact  that  the  apparent  hydrogen  ion 
concentration  as  determined  with  the  hydrogen  electrode  may  be 
raised  above  the  quantity  of  available  acid  present  by  the  addi- 
tion of  sufficient  salt.  To  deal  with  such  questions  without  trac- 
ing back  through  the  subtleties  of  certain  tacit  assumptions  is  a 
most  pernicious  practice.  It  seems  wiser  to  admit  at  once  that 
certain  of  the  more  fundamental  assumptions  are  too  insecurely 
based  to  provide  any  adequate  systematic  treatment  at  the  present 
time,  and  for  this  reason  such  questions  as  the  salt  error  of  indi- 
cators will  be  given  in  the  subsequent  chapters  what  may  at  first 
appear  to  be  too  brief  a  treatment.  Experimentally  the  safest 
procedure  to  follow  whenever  the  conduct  of  strong  electrolytes 
enters  into  the  determination  of  or  the  use  of  pH  values  is  stand- 
ardization of  data. 

Standardization  of  experimental  data  on  the  one  hand  and  the 
maintenance  of  the  more  simple  concepts  of  the  theory  of  electro- 
lytic dissociation  will  then  be  the  policy  of  the  following  treatment. 

SUPPLEMENTARY  REFERENCES 

A  few  references  on  the  conduct  of  "strong  electrolytes"  and  the  "activity" 
concept.  Arrhenius  (1887,  1914),  Beattie  (1920),  Bjerrum  (1919), 
Bronsted  (1919-1922),  Ebert  (1921,)*  Ferguson  (1916),  Ferguson- 
France  (1921),  Getman  (1920),  Ghosh  (1921),  Harkins  (1920),  Harned 
(1916,  1920,  1922),  Hill  (1921),  Jahn  (1900),  Kendall  (1921,  1922), 
Kraus  (1920, 1921),  Lapworth  (1915),  Lewis  (1907-1922),  Linhart  (1917, 
1919),  Noyes  (1907),  Noyes-Maclnnes  (1920),  Maclnnes  (1919), 
Rabinowitsch  (1921),  Stern  (1922).  Symposium  on  theory  of  electro- 
lytic dissociation  Trans.  Faraday  Society  15,  1-178,  Dec.  1919. 

pH  calculator.    Klopsteg  (1921). 

pH  tables  and  graphs.  Appendix  table  b.  Matula  (1916),  Roaf  (1920), 
Schmidt-Hoagland  (1919),  Symes  (1916). 

*  Contains  extensive  review. 


CHAPTER  III 

Outline  op  a  Colorimetric  Method 

Acidimetric-alkalimetric  indicators  are  substances,  the  colors 
of  which  correlate  with  the  hydrogen  ion  concentrations  of  the 
i      aqueous  solutions  in  which  they  are  dissolved. 

For  each  indicator  there  is  a  characteristic  pH  zone.  On  the 
acid  side  of  this  zone  the  indicator  is  completely  transformed  into 
its  "acid  color"  and  on  the  alkaline  side  of  this  zone  the  indicator 
is  completely  transformed  into  its  "alkaline  color."  Within  the 
characteristic  pH  zone  there  may  be  observed  different  proportions 
of  the  acid  and  alkaline  colors. 

In  ordinary  titrations  conditions  are  so  chosen  that  when  the 
"end-point"  of  the  titration  is  reached  the  pH  of  the  solution 
passes  suddenly  through  the  whole  range  of  the  indicator's  color- 
change.  The  intermediate  stages,  if  observed,  are  not  emphasized. 
The  intermediate  colors,  however,  are  the  important  ones  for  the 
present  purpose.  They  can  be  maintained  with  buffer  solutions; 
and,  being  characteristic  at  definite  pH  values,  they  can  be  used 
to  estimate  the  pH  of  tested  solutions  by  a  system  of  comparison 
with  standards.  To  distinguish  the  stabilized  degree  of  color 
transformation  from  the  changing  color  observed  during  a  titra- 
.  tion,  we  shall  adopt  S0rensen's  term  and  speak  of  the  virage  of 
an  indicator  when  referring  to  a  particular,  stabilized  degree  of 
color  transformation. 

For  reasons  which  will  be  given  in  Chapter  IV  the  characteristic 
pH  zone,  within  which  differences  of  virage  may  be  observed,  is 
comparatively  narrow.  It  is  therefore  necessary  to  have  a  series 
of  indicators,  the  zones  of  which  overlap  (see  table  on  page  80). 
Then  if  an  indicator  is  found  to  be  transformed  completely  to  its 
acid  color  by  a  solution  under  test,  the  indicator  next  in  the  series 
is  tried  and  so  on  until  there  is  found  the  indicator  which  is  trans- 
formed by  the  solution  'to  an  intermediate  virage.  It  is  then 
known  that  the  solution  has  a  pH  value  within  the  limits  char- 
acteristic of  the  indicator  used. 

For  some  purposes  it  is  sufficient  to  know  the  approximate  pH 
and  this  may  be  estimated  from  the  degree  of  color  transformation 

48 


OUTLINE   OF   COLORIMETRIC   METHOD  49 

induced  in  the  indicator.     It  is  a  simple  matter,  however,  to  take 
the  first  step  toward  accuracy.     This  is  done  as  follows. 

There  have  been  determined  by  hydrogen-electrode  methods 
the  pH  values  of  definite  buffer  solutions  such  as  mixtures  of 
KH2PO4  and  Na2HP04.  Series  of  such  solutions  and  the  details 
of  their  preparation  are  described  in  Chapter  VI.  By  adding 
definite  quantities  of  an  indicator  to  definite  volumes  of  these 
standard  solutions  a  series  of  color  standards  is  easily  prepared. 
With  these  standards  the  color  of  the  tested  solution  can  be 
compared.  For  instance,  suppose  that  the  preliminary  test  of  a 
given  solution  has  shown  that  it  transforms  the  indicator  phenol 
red  neither  to  a  full  red  nor  to  a  bright  yellow  but  that  the  pro- 
portion of  red  is  low.  Previous  experience  has  impressed  the  fact 
that  such  a  virage  with  phenol  red  indicates  the  solution  to  be  near 
pH  7.0.  See  the  color  chart.  Therefore,  one  employs  those 
standard  buffer  solutions  giving  pH  values  near  7.0.  To  a  series 
Df  uniform  test  tubes  is  added  seriatim  10  cc.  of  each  of  the 
standard  phosphate  solutions  described  in  Chapter  VI.  To  each 
:ube  is  added  five  drops  of  phenol  red  solution.  On  mixing  there 
vill  be  observed  a  graded  series  of  virages  and  perhaps  three  of 
;hem  will  be  recognized  at  once  to  have  nearly  the  same  color  as 
10  cc.  of  the  tested  solution  mixed  with  5  drops  of  the  same  indi- 
;ator  solution.  When  closer  inspection  shows  where  the  color- 
natch  occurs,  the  standard  with  its  known  pH  value  and  the 
ested  solution  are  supposed  to  have  the  same  pH  value.  As  in 
his  example,  it  is  always  necessary  to  make  comparisons  between 
,ike  concentrations  of  indicator  viewed  through  equal  depths  of 
s  olution. 

Anerrorjnay  be  made  if  the  standard  and  tested  solutions      / 
i  liffer  much  in  total  salt  concentration,  or  if  the  tested  solution 
i  ontains  much  protein,  or  if  an  unreliable  indicator  is  used.     But 
\  fe  shall  have  to  deal  with  these  and  other  difficulties  in  subse- 
(  uent  chapters. 

When  one  is  familiar  with  the  virages  of  the  indicators  at 
]  nown  pH  values  very  fair  estimations  may  be  made  without  the 
i  id  of  the  standards;  but  there  is  no  way  as  satisfactory  as  the 
{ stting  up  of  the  standards  for  the  establishment  of  a  correct 
i  npression  of  the  relations  of  the  various  indicators  on  the  pH 


50  THE   DETERMINATION    OF   HYDROGEN    IONS 

scale.  On  the  other  hand,  the  author  has  discovered  in  his 
conversations  that  there  are  a  great  many  investigators  who 
would  like  to  use  indicators  for  the  occasional  rough  measurement 
of  pH  but  who  are  discouraged  by  a  pressure  of  work  which  pre- 
vents them  from  taking  the  time  to  carefully  prepare  the  standard 
solutions.  To  furnish  such  investigators  with  a  demonstration  of 
the  general  relations  of  the  various  indicators  and  to  furnish 
rough  standards  the  attempt  has  been  made  in  figure  8,  to  repro- 
duce the  colors.  The  colors  of  standard  buffer  solutions  con- 
taining definite  quantities  of  the  several  indicators  were  reproduced 
very  faithfully  by  Mr.  Max  Broedel  of  the  Johns  Hopkins  Medical 
School.  It  must  be  remembered,  however,  that  in  undertaking  a 
second  reproduction  by  means  of  the  printer's  art  the  publishers 
are  to  be  commended  for  their  courage  and  are  not  to  be  held 
responsible  for  the  inadequacy  of  the  result.  Aside  from  the 
inherent  difficulty  in  freeing  a  printed  color  from  the  effect  of  the 
vehicle,  there  remains  the  utter  impossibility  of  reproducing  upon 
paper  the  exact  virage  observed  in  a  liquid  solution.  The  funda- 
mental phenomena  are  quantitatively  very  different  in  the  two 
cases.  Therefore  the  user  of  the  chart  of  colors  will  have  to  use 
discretion  and  some  imagination.  If  he  does  not  attempt  to 
make  the  reproductions  take  the  place  of  the  standards  he  should 
find  them  useful  for  class  room  demonstrations,  for  refreshing  the 
memory  and  for  rough  standards.1 

In  each  case  the  colors  were  reproduced  from  tubes  16  mm. 
internal  diameter  containing  10  cc.  standard  buffer  solution. 
The  quantities  of  indicator  solution  added  in  each  case  were  as 
follows:  Thymol  blue,  acid  range  (T.  B.  acid  range)  1  cc.  0.04 
per  cent  solution.  Brom  phenol  blue  (B.  P.  B.)  0.5  cc.  0.04  per 
cent  solution.  Methyl  red  (M.  R.)  0.3  cc.  0.02  per  cent  solution. 
Brom  cresol  purple  (B.  C.  P.)  0.5  cc.  0.04  per  cent  solution.  Brom 
thymol  blue  (B.  T.  B.)  0.5  cc.  0.04  per  cent  solution.  Phenol  red 
(P.  R.)  0.5  cc.  0.02  per  cent  solution.  Cresol  red  (C.  R.)  0.5  cc. 
0.02  per  cent  solution.  Thymol  blue  (T.  B.)  0.5  cc.  0.04  per  cent 
solution. 

1  Separates  of  the  color  chart  may  be  obtained  from  the  publisher. 


Dr.  Barnett  Cohen  of  the  Hygienic  Laboratory  has  recently 
(Public  Health  Reports,  U.  S.  P.  H.  S.,  38,  199,  1923)  synthe- 
sized the  following  new  sulfonphthalein.  Brom  cresol  green 
covers  the  range  of  methyl  red.  Salt  and  protein  errors  have 
not  yet  been  determined. 


CHEMICAL,   NAME 

8CGGESTED  COMMON  NAME 

APPARENT 

DISSOCIATION 

CONSTANT 

pH 

RANGE 

m-Cresol  sulfonphthalein 

Meta  cresol  purple 

2.8  X  lO"2 
5.0  X  10~9 

0.5-2.5 
7.6-9.2 

Dibromo-dichloro-phenol   sul- 
fonphthalein 
Tetra  bromo-m-cresol   sulfon- 

Brom-chlor phenol 

blue 
Brom  cresol  green 

7.9  X  lO"6 
1.0  X  10~5 

3.2-4.8 
4.0-5.6 

phthalein 

Dichloro-phenol  sulfonphtha- 
lein 

Dibromo-phenol  sulfonphtha- 
lein 

Chlor  phenol  red 
Brom  phenol  red 

8.9  X  10~7 
4.5  X  10~7 

5.0-6.6 
5.4-7.0 

OUTLINE    OF   COLORIMETRIC    METHOD  51 

The  ranges  of  pH  covered  by  the^  several  indicators  in  the 
color  chart  are: 

T.  B.  (acid  range),  Thymol  blue 1.2-2.8 

B.  P.  B.,  Brom  phenol  blue 3.0-4.6 

M.  R.,  Methyl  red 4.4-6.0 

B.  C.  P.,  Brom  cresol  purple 5.4-7.0 

B.  T.  B.,  Brom  thymol  blue 6.0-7.6 

P.  R.,  Phenol  red 6.6-8.2 

C.  R.,  Cresol  red 7.2-8.8 

T.  B.,  Thymol  blue 8.2-9.8 

For  class-room  work  it  is  advantageous  to  show  the  position 
of  the  several  indicators  on  the  pH  scale  by  relining  each  series 
so  that  corresponding  pH  values  overlap. 

One  requirement  for  the  colorimetric  method  is  a  set  of  indi- 
cators selected  for  their  relative  freedom  from  the  so-called  pro- 
tein and  salt  errors  and  for  their  brilliancy.  Beside  the  brilliant 
and  reliable  selection  of  Clark  and  Lubs  there  is  the  care- 
fully studied  selection  of  S0rensen  given  on  page  78  with  S0rensen's 
summary  of  properties  on  page  79. 

There  are  also  required  standard  buffer  solutions  whose  pH 
values  are  established  from  hydrogen  electrode  measurements. 
It  is  in  the  preparation  of  these  standards  that  the  greater  part 
of  the  labor  of  the  colorimetric  method  is  involved ;  but,  once  the 
stock  solutions  are  carefully  made,  the  preparation  of  the  mix- 
tures is  a  simple  matter.  If  only  the  pH  range  5.2  to  8.0  is 
necessary,  the  S0rensen  mixtures  of  primary  and  secondary  phos- 
phates are  the  more  convenient.  If  a  wider  range  is  desired  the 
system  tabulated  on  pages  106  to  107  is  recommended. 

For  precise  measurements  there  are  required  control  by  hydro- 
gen electrode  measurements  and  constant  watchfulness  for  the 
several  sources  of  error  noted  in  following  chapters.  Approximate 
methods  are  described  in  Chapter  VIII. 

In  figure  7  are  shown  several  pieces  of  equipment  useful  in 
colorimetric  work.  Beginning  at  the  left  is,  first,  a  sample  of 
a  litre  bottle  used  for  holding  the  standard  stock  solutions,  such 
as  M/5  KH  Phthalate,  which  are  not  seriously  affected  by  expo- 
sure to  the  carbon  dioxide  of  the  laboratory  air.  In  Clark  and 
Lubs'  series  of  standards  (see  page  99)  there  are  required  four 
such  bottles.     In  this  same  series  there  is  required  a  container  for 


C3  - 


6  f 


OUTLINE   OF   COLORIMETRIC    METHOD  53 

standard  M/5  NaOH.  This  should  be  a  paraffined  bottle  with 
calibrated  burette  and  soda-lime  guard-tubes  attached. 

In  figure  7  there  is  next  shown  a  comparator  whose  construc- 
tion is  given  on  page  70.  This  is  used  in  comparing  turbid  or 
colored  solutions  with  the  standards.  When  the  turbidity  of  a 
tested  solution  brings  into  evidence  the  dichromatism  of  an  indi- 
cator as  described  on  page  65,  the  comparator  is  used  with  the 
light  screen  shown  at  the  back  of  figure  7  and  described  on  page  67. 

For  ordinary  colorimetric  comparisons  the  test  tube  rack  shown 
in  the  figure  is  very  useful.  The  holders  are  the  clips  sold  at 
stationers  for  holding  rubber  stamps.  Two  forms  of  dropping 
bottle  are  next  shown  and,  finally,  at  the  right,  two  paraffined 
bottles  for  alkaline  standards  and  two  acid  resistant  bottles  for 
acid  solution.  Of  such  bottles  there  are  required  for  the  series 
of  standards  given  on  pages  106-107  fifty-one  bottles  and  the  same 
number  of  10  cc.  pipettes.  The  range  of  pH  thus  covered  is  wider 
than  that  called  for  in  special  investigations.  The  pipettes  may 
have  their  tips  broken  to  allow  quicker  delivery  of  solution  with- 
out serious  violation  of  volume  requirements.  S0rensen's  stand- 
ards, pages  111-114,  are  designed  so  that  individual  10  cc.  samples 
are  made  up  as  required.  Larger  quantities  such  as  are  specified 
in  table  21  provide  for  the  occasional  test. 


CHAPTER  IV 

Theory  of  Indicators 
Les  proprUUs  des  corps  sont  les  proprUUs  des  nombres.—T>E  Chancotjrtois. 

Indicator  theory  is  a  cross-roads  where  the  cultivators  of 
distinct  fields  of  science  meet.  Here  comes  the  organic  chemist 
with  analyses  of  plant  and  animal  products,  structural  formulas 
of  synthetic  dyes,  tautomers  and  chromophores.  Here  comes  the 
physico-chemist  with  formulations  of  electrolytic  and  tautomeric 
equilibria.  Here  comes  the  physicist  with  the  theory  of  color  and 
the  instruments  of  light  analysis.  And  perhaps  there  will  meet 
here  the  psychologist  bringing  a  clearer  description  of  the  sub- 
jective aspect.  As  a  confluence  of  trade  routes  may  determine  the 
growth  of  a  city  so  the  confluence  of  many  specialties  may  some- 
time lead  to  a  great  community  of  interest  where  the  cross-roads 
of  indicator  theory  once  lay.  Indicators  themselves  are  not 
particularly  unique  except  that  they  compel  the  attention  of  the 
eye.  Through  this  we  are  made  aware  of  phenomena  of  wide 
occurrence. 

According  to  the  inclination  of  a  reviewer  one  or  another  of 
the  manifold  aspects  of  indicator  theory  might  be  emphasized. 
"'  We  must  choose  that  which  is  useful  to  the  purpose  at  hand  and 
for  the  sake  of  a  necessary  brevity  we  must  try  to  include  only 
so  much  as  will  contribute  toward  an  intelligent  use  of  indicators 
as  tools  for  the  determination  of  hydrogen  ion  concentration. 

In  the  first  place  it  may  be  said  that  the  customary  manner  of 
using  indicators  is  merely  a  method  of  comparison  involving  little 
if  any  theory.  The  conduct  of  an  indicator  may  be,  and  generally 
is,  ."calibrated"  by  means  of  hydrogen  electrode  measurements. 
It  is  well  to  emphasize  this  uninspiring,  matter-of-fact  aspect 
because  it  will  remind  us  that  with  so  much  of  the  fundamental 
theory  at  hand  the  employment  of  theory  may  lead  to  a  wider 
usefulness  of  the  instruments  thus  far  treated  empirically.  But 
before  this  can  be  done  important  relationships  must  be  ex- 
pressed definitely  in  numerical  data.  How  this  can  be  done  is 
the  immediate  problem  before  us. 

54 


THEORY   OF   INDICATORS 


55 


The  first  consistent  attempt  to  bring  the  conduct  of  indicators 
into  relation  with  electrolytic  dissociation  was  that  of  Ostwald 
(1891).  .He  assumed  that  indicators  are  acids  or  bases  the  undis- 
sociated  molecules  of  which  have  a  color  different  from  that  of  their 
dissociation  products.     If  this  be  so,  it  is  evident  that  the  color 


TABLE  4 
Approximate  apparent  dissociation  constants  of  indicators 


Phenol  sulfon  phthalein 

o-Cresol  sulfon  phthalein 

Thymol  sulfon  phthalein 

Carvacrol  sulfon  phthalein 

a-Nap&hol  sulfon  phthalein 

Tetra  bromo  phenol  sulfon  phthalein. 
Di  bromo  o-cresol  sulfon  phthalein. . . 

Di  bromo  thymol  sulfon  phthalein 

Phenol  phthalein 

o-Cresol  phthalein 

a-Naphthol  phthalein 

Methyl  red 

Ethyl  red 

Propyl  red 

Thymol  sulfon  phthalein  (acid  range) . 


Ka 


.2  X  10" 
.0  X  10" 


10" 
10" 
10" 

io- 

10" 


.2  X 

0  X 

3  X 

9  X 

0  X 

0  X  io- 
0  X  io- 

0  X  10" 

0  X  io- 

9  X  10- 

0  X  io- 

0  X  10" 

o  x  io- 


pKa 


7.9 

8.3 

8.9 

9.0 

8.2 

4.1 

6.3 

7.0 

9.7* 

9.4 

8.4 

5. If 

5.4 

5.4f 

1.7 


*  This  value  is  identical  with  Rosenstein's  (1912). 

t  In  the  table  published  in  the  Journal  of  the  Washington  Academy, 
vol.  vi,  p.  485,  these  values  for  methyl  red  and  propyl  red  were  erroneously 
interchanged. 

Tizard  (1910)  gives  Ka  =  1.05  X  10"6  or  pK  -  4.98  for  methyl  red 
considered  as  an  acid. 

of  an  indicator  should  change  with  the  pH  of  a  solution. exactly 
as  the  dissociation  curves  described  in  Chapter  I.  If,  for  in- 
stance, the  indicator  is  an  acid,  colorless  in  the  undissociated 
form,  but  colored  when  dissociated  as  an  anion,  then  the  change 
of  color  with  the  hydrogen  ion  concentration  should  conform  to 
the  equation: 


Ka  +  [H+] 


where  Ka  is  the  dissociation  constant  of  the  acid  indicator  and 
a  is  the  degree  of  dissociation.     Assuming  then  that  such  a  rela- 


56 


THE  DETERMINATION  OF  HYDROGEN  IONS 


tion  does  hold,  let  us  determine  Ka  for  a  series  of  indicators  in 
the  following  way. 

From  the  above  equation  when  «  =  §,  Ka  =  [H+].  That  is, 
at  a  hydrogen  ion  concentration  corresponding  numerically  to  the 
dissociation  constant,  the  acid  is  half  dissociated.  At  such  a 
hydrogen  ion  concentration  a  colorless-to-red  indicator,  such  as 
phenolphthalein,  should  show  half  the  available  color;  and  a 
yellow-to-red  indicator,  such  as  phenol  red,  should  show  the  half- 
yellow,  half-red  state.  We  can  match  the  half  way  state  of  this 
first  solution  by  superimposing  two  solutions  each  of  a  depth 
equal  to  the  first,  if  we  have  in  one  of  the  superimposed  solutions 
only  the  yellow  form  and  in  the  other  only  the  red  form,  each 
concentration  equaling  half  the  concentration  in  the  first  solution. 
Such  an  arrangement  is  shown  diagraphically  in  the  following 
figure : 


i 


i 


Alkaline  solution    (full 
red)  5  drops  indicator 


Known    pH    standard 
10  drops  indicator 


Acid  solution  (full  yel- 
low) 5  drops  indicator 


Water  blank 


We  may  not  know  at  the  beginning  at  what  pH  the  half  trans- 
formation may  occur,  so  we  vary  the  pH  of  the  standard  solution 
until  a  match  with  our  superimposed  solutions  does  occur.  Then 
we  have  found,  presumably,  the  hydrogen  ion  concentration  the 
numerical  value  of  which  is  the  dissociation  constant  of  the 
indicator.  Values  so  obtained  by  Clark  and  Lubs  (1917)  are  given 
in  table  4. 


THEORY   OF   INDICATORS  57 

<  As  indicated  in  Chapter  I  the  determination  of  the  dissociation 
curve,  or  of  the  half  transformation  point,  does  not  tell  us  whether 
we  are  dealing  with  the  dissociation  curve  of  an  acid  or  the  disso- 
ciation-residue curve  of  a  base  or  vice  versa.  Thus  methyl  red 
is  treated  in  table  4  as  an  acid  and  plotted  in  figure  9  as  if  the 
color  were  associated  with  the  undissociated  form.  Methyl  red 
however  could  be  treated  as  a  base. 
Just  as  it  is  convenient  to  deal  with  a  logarithmic  function  of 

[H+]  so  the  dissociation  constants  can  be  used  in  the  form  log  — 

This  can  be  designated  pKa. 

Gillespie  (1920)  gives  somewhat  different  values  but,  since  the 
method  used  in  each  case  was  approximate,  the  table  given  above, 
as  it  is^found  in  the  paper  by  Clark  and  Lubs  (1917)  will  do  for 
purposes  of  illustration.  With  the  aid  of  the  approximately 
determined  apparent  dissociation  constants  we  are  enabled  to 
plot  the  curves  shown  in  figure  9,  which  reveal  graphically  the 
relationships  of  the  various  indicators  in  the  series  we  shall  dis- 
cuss. This  figure  shows  at  a  glance  that  an  indicator  of  the 
simple  type  we  have  assumed  has  no  appreciable  dissociation  and 
consequently  exists  in  only  one  colored  form  at  pH  values  begin- 
ning about  2  points  below  the  half  transformation  point,  while  at 
the  same  distance  above  this  point  the  indicator  is  completely 
dissociated  and  exists  only  in  its  second  form.  Between  these 
limits  the  color  changes  may  be  observed.  The  useful  range  of 
such  an  indicator  is  far  less  than  4  pH  units  for  optical  reasons 
which  will  be  discussed  later. 

The  illustration  (fig.  9)  will  show  how  in  choosing  a  set  of  indi- 
cators it  is  advantageous  to  include  a  sufficient  number,  if  reli- 
able indicators  can  be  found,  so  that  their  ranges  overlap.  It 
shows  that  each  of  the  indicators,  when  considered  to  be  of  the 
simple  type  we  have  assumed,  has  an  equal  range.  It  also  shows 
that  the  half  transformation  point  of  each  indicator  occurs  nearer 
one  end  of  the  useful  range,  the  useful  range  being  indicated  by 
the  shaded  part  of  the  curve.     This  aspect  will  be  discussed  later. 

It  is  evident  that  if  the  actual  color  change  of  an  indicator  varied 
with  pH  in  accordance  with  a  curve  such  as  those  in  figure  9, 
and  if  the  true  dissociation  constant  were  accurately  known,  then 
the  hydrogen  ion  concentration  of  a  solution  could  be  determined 


<^- 


1 

/ 

GASTB1 C 

JUICS 

^ 

2 

YEAST 
LIMIT 

3 

WIKES 

4 

CASEIN  ISO- 
ELECTRIC PT. 

i^L 

X/C 

6 

•*r" 

ii 

7 

*s,<i* 

^V 

SEA 
WATER 

vl 

^s^ 

10        ^ 

11 

\ 

Z$      „      SO  7S 

%   DISSOCIATION 


1^10  HCJ 


B.PARA  TYPHI  ACCL. 

B. TYPHI  Afl«L. 
B.COLI  LIMIT 
PBEUMOCOCOTS  AGCL. 


M/2 


yiO  MH4OH 


too 


Fia.    9.  Indicator   Curves   and    Significant   pH    Values.    Shading 
Indicates  Useful  Range 


58 


THEORY   OF   INDICATORS  59 

by  finding  the  percentage  transformation  induced  in  the  indicator. 
Indeed  the  dissociation  constants  of  some  few  indicators  have 
been  determined  with  sufficient  accuracy  to  permit  the  use  of 
this  method  when  the  proper  means  of  determining  the  color 
intensities  are  used.     This  will  be  discussed  in  Chapter  VIII.    R 

We  have  been  assuming  that  thejtheory  of  indicators  may  be 
treated  in  the  simple  manner  originally  outlined  by  Ostwald 
(1891).  In  his  theory  it  was  assumed  that  the  anion  of  an  indi- 
cator acid,  for  instance,  has  a  color  different  from  that  of  the 
undissociated  molecule.  This  assumption  if  unmodified  does  not 
harmonize  with  what  is  known.  Researches  in  the  phenomena  of 
jtautomerism  have  shown  that  when  a  change  in  color  is  observed 
in  an  indicator  solution  the  change  is  associated  with  the  forma- 
tion of  a  new  substance  which  is  generally  a  molecular  rearrange- 
ment or  so-called  "tautomer"  of  the  old.  If  this  color  change  is 
associated  with  the  transformation  of  one  substance  into  another, 
how  is  it  that  it  seems  to  be  controlled  by  the  hydrogen  ion  con- 
centration of  the  solution?  As  Steiglitz  (1903)  and  others  have 
pointed  out,  it  is  the  state  of  these  compounds,  their  existence  in 
a  dissociated  or  undissociated  condition,  which  determines  the 
stability  of  any  one  form. 

The  method  of  dealing  with  the  tautomeric  relations  of  indi- 
cators is  shown  by  the  following  quotation  from  Noyes  (1910) : 

We  may  derive  a  general  expression  (as  has  previously  been  done  by 
Acree,  1907)  for  the  equilibrium-relations  of  any  pair  of  tautomeric  acids 
and  their  ions.  The  three  fundamental  equilibrium  equations  are  as 
follows: 

eaaci.K/.  (20)     (H+)  aid  - K* .  (21) 

(HIn')  "     (  (HIn")  K  »»     **" 

2S2-&-     (22) 
(HInO        Kt'     (22j 

Multiplying  (21)  bv  (22),  adding  (20)  to  the  product,  and  substituting  in 

♦     t      ,ttt   rx  -,        ,      (HlnQ  +  (HIn' 

tor  for  (HIn  )  its  value — 

1  +  KT 

(H+)  [(In'")  +  (In'")]       K',  +  K",  K, 


fTTTnM  -I-  fTTTn'M 

the  denominator  for  (HIn')  its  value — — — given  by  (22),  we  get 

1  +  KT 


(HInO  •+  (HIn")  1  +  K, 


=  KIA  (23) 


If  the  indicator  is  a  base  existing  as  the  two  tautomeric  substances 
fn'OH  and  In"OH,  having  ionization  constants  K'r  and  K"i  and  a  tau- 
tomer constant  KT  denned  by  equations  analogous  to  (20),  (21)  and  (22),  the 


60  THE   DETERMINATION    OF   HYDROGEN   IONS 

general  expression  for  the  equilibrium  between  the  ionized  bases  and  their 
ions  is: 

(OH")  [(In'+)  +  (Iny+)]     -K'x+K'xKt 


(In' OH)  +  (In'OH)  1  +  KT 


=  KIB  (24) 


In  these  expressions  a  single  constant  KIA  or  KIB  has  been  introduced  in 
place  of  the  function  of  the  three  constants  K'x,  K"i,  and  KT  .  .  .  • 
The  constant  so  calculated  for  a  pair  of  tautomeric  acids  or  bases  can  evi- 
dently be  substituted  for  the  ionization  constant  of  an  ordinary  (non  tau- 
tomeric) acid  in  any  derived  expression,  provided  the  sum  of  the  two  ion 
concentrations  and  the  sum  of  the  two  acid  or  base  concentrations  are  quan- 
tities that  are  to  be  known  or  are  to  be  calculated. 

If  then  in  equation  (23)  we  substitute  (In-)  for  [(In'~~)  -+-  (In"~)]  and 
(HIn)  for  [(HIn')  +  (HIn")]  we  have: 

(HIn)       "  KlA  (25) 

Applying  to  Noyes'  equation  (25)  the  derivation  given  on  page  25 
we  have 

KIA  +  (H+)' 

From  this  we  may  plot  the  curves  of  figure  9.  Such  curves  will 
then  represent  the  color  transformations  when  and  only  when 
(In-)  is  substantially  equal  to  (In'-)  or  to  (In"-),  whichever 
tautomer  is  associated  with  the  color.  The  most  probable  expla- 
nation of  the  fact  that  such  curves  do  represent  very  closely  the 
color  transformations  in  certain  instances  is  that  KT  (see  equation 
(23))  is  so  small  that  the  dissociation  brought  about  by  salt  for- 
mation leaves  (In-)  dominant. 

In  other  words  it  is,  after  all,  the  degree  of  dissociation,  as 
determined  by  the  hydrogen  ion  concentration,  that  determines 
which  tautomer  predominates.  Therefore,  consideration  of  the 
tautomeric  equilibria  only  modifies  the  original  Ostwald  treat- 
ment to  this  extent :  the  true  dissociation  constant  is  a  function  of 
the  several  equilibrium  and  ionization  constants  involving  the 
different  tautomers  and  must  be  replaced  by  what  Acree  calls  the 
"total  affinity  constant,"  or  by  what  Noyes  calls  the  "apparent 
dissociation  constant,"  when  it  is  desired  to  show  directly  how 
the  color  depends  upon  the  hydrogen  ion  concentration. 

Many  indicators  are  poly-acidic  or  poly-basic  and  will  not 
rigidly  conform  to  the  treatment  for  a  simple  monovalent  acid 
such  as  we  have  described.  Phenolphthalein,  for  instance,  as 
was  shown  by  Acree  (1908)  and  by  Wegscheider  (1908)  must  be 


THEORY   OF   INDICATORS 


61 


considered  as  poly-acidic.  The  proper  equations  to  apply 
in  this  case  have  been  given  by  Acree  (1907,  1908)  and  also  by 
Wegscheider  (1908,  1915).  According  to  Acree  and  his  students 
(Acree,  1908)  (Acree  and  Slagle,  1909)  the  chief  color  change  in 
phenolphthalein  is  associated  with  the  presence  of  a  quinone 
group  and  with  the  ionization  of  one  of  the  phenol  groups.  In 
the  sulfon  phthalein  series  of  indicators  Acree  and  his  students 
(White,  1915,  and  White  and  Acree,  1918)  have  found  much  the 
same  sort  of  condition. 

In  the  sulfon  phthalein  series,  however,  certain  unique  proper- 
ties described  by  Lubs  and  Acree  (1916)  make  the  series  eminently 
suited  for  experimental  demonstration  of  the  seat  of  color  change. 

In  the  sulfon  phthalein  group  of  indicators  we  have  to  deal 
with  poly-acids;  but  as  Acree  has  shown,  the  dissociation  con- 
stant of  the  strong  sulfonic  acid  group  is  so  very  much  greater 
than  that  of  the  weak  phenolic  group,  with  which  the  principal 
color  change  is  associated,  that  there  is  no  serious  interference. 
As  shown  in  Chapter  I  we  may,  therefore,  plot  the  curves  for  the 
chief  color-changes  as  if  we  were  dealing  with  monobasic  acids. 

The  structures  of  all  the  sulfon  phthaleins  are  analogous  to 
that  of  phenol  sulfon  phthalein  (phenol  red)  whose  various  tau- 
:omers  are  given  by  Lubs  and  Acree  (1916)  in  the  following 
scheme : 

C6H4OH 
I 
:6H4-C(C6H4OH)2  -»  C6H4-C-C6H4OK  -*  C6H4-C(C6H4OK)2 
II'  II  II 

302  -  O  S02  -  O  S02  -  O 

A  colorless  B  colorless  C  colorless 


C6H4OH 

I 
^6H4  —  C :  CeEU :  O 
I 

302-OH 
)  slightly  colored 


C6H4OH 

I 
CeH4  —  C :  CeH4 : 0 
I 

S020-  +  H+ 
E  slightly  colored 


C6H40-K+ 
l         I      I 
CeH4  —  C :  CeH4 : 0 


C6H4OH 

I 
— ►    CeH4  —  C '.  C6H4 !  O 
I 

S020-  +  K+ 
F  slightly  colored 

i  ■ 

C6H40-+K+ 
I 
CeH4  —  C  i  CeH4  lO 


S020"  +  K+ 
H  deeply  colored 


S020-  +  K+ 
G  deeply  colored 


62  THE  DETERMINATION  OF  HYDROGEN  IONS 

The  colorless  lactoid  A  by  reason  of  the  strong  tendency  of 
the  sulfonic  acid  group  to  ionize  goes  over  into  the  quinoid  struc- 
tures illustrated  in  the  second  line  which  are  slightly  colored 
yellow.  It  is  the  transformation  of  F  to  G  and  H,  the  ionization 
of  the  phenolic  group  forming  a  quinone-phenolate  structure 
which  correlates  with  the  intense  red  color  of  phenol  sulfon 
phthalein  (phenol  red). 

Just  as  the  discovery  of  tautomerism  seemed  at  first  to  discredit 
the  original  form  of  the  Ostwald  theory  of  color  change,  so  it  is 
now  realized  that  a  mere  change  in  structure  is  of  itself  quite 
inadequate  to  account  for  the  change  in  the  light  absorption  upon 
which  the  color  of  a  solution  depends.  Light  is  an  electro- 
magnetic phenomenon  and  the  absorption  of  the  energy  in  any 
particular  train  of  light  is  undoubtedly  due  to  the  resonance  of 
electrons.  Thus  the  direct  connection  between  light  absorption 
and  molecular  structure  will  be  found  in  the  relation  of  molecular 
structure  to  the  distribution  and  freedom  of  the  component 
electrons.  It  is  in  this  direction  that  Baly  (1915)  believes  a 
satisfying  theory  of  the  colors  of  dyes  will  be  found.  Although 
Baly  has  called  attention  to  difficulties  in  the  correlation  of  colors 
with  tautomeric  changes  there  seems  to  be  no  inherent  reason 
why  tautomerism,  alteration  of  the  fields  of  force  within  the 
molecule,  electrolytic  ionization  and  color  should  not  be  corre- 
lated. The  original  Ostwald  theory  may  yet  prove  to  be  essen- 
tially correct  in  that  the  charging  of  a  molecule  by  ionization 
should  cause  a  redistribution  of  the  fields  of  force.  Whether  or 
not  a  molecular  rearrangement  or  absorption  of  a  particular  train 
of  visible  light  follows  may  well  depend  upon  particular  cir- 
cumstances. But  of  course  all  this  is  left  to  the  future  and  to 
quantitative  data. 

OPTICAL   ASPECTS 

While  the  color  changes  of  indicators  are  correlated  with  molec- 
ular rearrangements  controlled  by  hydrogen  ion  concentrations, 
it  should  not  be  forgotten  that  the  phenomena  observed  are  opti- 
cal and  tnat  no  theory  of  indicators  can  be  considered  complete 
enough  for  practical  purposes  which  fails  to  recognize  this.  As 
ordinarily   observed   in   laboratory   vessels   the   color   observed 


THEORY    OF   INDICATORS  63 

is  due  to  a  somewhat  complex  set  of  phenomena.  It  is  unfortu- 
nate that  we  have  no  adequate  treatment  of  the  subject  which 
at  the  same  time  embraces  electrolytic  dissociation,  tautomerism 
and  the  optical  phenomena  in  a  manner  directly  available  in  the 
practical  application  of  indicators.  The  simultaneous  treatment 
of  these  various  aspects  is  necessary  before  we  can  feel  quite 
sure  of  our  ground  when  dealing  with  discrepancies  often 
observed  in  the  comparison  of  colorimetric  and  electrometric 
measurements  of  biological  fluids. 

Let  us  first  consider  the  range  of  an  indicator  as  it  is  determined 
by  the  differentiating  power  of  the  eye.  An  approximate  treat- 
ment of  this  is  all  that  will  be  attempted. 

Using  equation  (10),  cf.  page  26: 

1  a 

pH  =  log  —  +  log 


K  (1  -  a) 

we  find  on  differentiation  that  the  rate  of  increase  in  a   with 
increase  of  pH  is: 


da 


d(PH) 
When 


a. 


a  (1  —  a). 


-  0,  a  -  i< 


d(pH)2  2 

In  other  words  the  maximum  rate  of  increase  in  dissociation  is  at 
the  half  transformation  point.  This  fixes  a  reference  point  when 
indicators  are  to  be  employed  in  distinguishing  differences  in  pH. 
The  question  now  arises  whether  or  not  this  is  the  central  point 
oi  the  optimal  conditions  for  differentiation  of  pH  values.  It 
may  be  said  at  once  that  it  is  not,  because  the  eye  has  not  only 
to  detect  differences  but  also  to  resolve  these  differences  from  the 
3olor  already  present.  Experience  shows  that  the  point  of  maxi- 
mum rate  of  increase  in  a  is  near  one  limit  of  the  useful  range  and 
'hat  this  range  lies  on  the  side  of  lower  color.  Thus,  in 
:he  case  of  the  one-color  indicator  phenolphthalein,  the  useful 
?one  lies  between  about  8.4  and  9.8  instead  of  being  cen- 
tred at  9.7  which  corresponds  with  the  point  of  half-transforma- 
ion.     In  the  case  of  a  two-color  indicator  such  as  phenol  red  the 


64  THE   DETERMINATION   OF   HYDROGEN   IONS 

same  reasoning  holds,  because  the  eye  instinctively  fixes  upon  the 
very  dominant  red.  With  other  two-color  indicators  the  principle 
holds  except  when  there  is  no  very  great  difference  in  the  com- 
mand upon  the  attention  by  one  or  the  other  color. 

It  should  be  mentioned  however  that  these  more  or  less  empiri- 
cal relations  are  observed  in  comparing  virages  at  equal  incre- 
ments of  pH  when  the  indicator  concentration  is  adjusted  to 
emphasize  the  differences  among  the  less  intensely  colored  tubes. 
By  suitable  dilution  of  the  indicator  the  differences  among  the 
tubes  having  the  higher  percentage  color  may  be  emphasized 
and  the  useful  range  of  the  indicator  slightly  extended.  In  prac- 
tice this  is  a  procedure  which  requires  care  for  it  is  easy  to  be- 
come confused  when  dealing  with  different  concentrations  of  the 
same  indicator. 

The  fixing  of  the  lower  limit  of  usefulness  of  a  given  indicator 
involves  another  factor.  There  is  the  question  of  the  total 
indicator  which  may  be  brought  into  action.  A  dilute  solution 
of  phenolphthalein  may  appear  quite  colorless  at  pH  8.4  while 
a  much  stronger  solution  will  show  a  distinct  color  which  would 
permit  distinguishing  8.2  from  8.4.  But  the  concentration  is 
limited  by  the  solubility  of  the  indicator  and  therefore  must  be 
taken  into  consideration.  In  short  there  is  no  basis  upon  which 
to  fix  definite  limits  to  the  pH  range  of  a  given  indicator,  and 
those  limits  which  are  given  must  be  considered  to  be  arbitrary. 
On  the  other  hand  the.  apparent  dissociation  curve  is  quite 
definitive;  and  were  it  not  for  the  greater  convenience  of  the 
"range  of  usefulness"  it  would  be  preferable  to  define  the  charac- 
teristics of  an  indicator  in  terms  of  its  apparent  dissociation 
constant. 

We  ordinarily  speak  of  color  as  it  if  were  an  entity.  As  a  mat- 
ter of  fact  the  color  exhibited  by  an  indicator  in  solution  is  due  to 
the  selective  absorption  of  certain  frequencies  of  the  incident 
light.  This  results  in  the  partial  or  complete  blocking  off  of  the 
light  in  one  or  more  regions  of  the  spectrum,  as  may  be  seen  by 
the  dark  band  or  bands  which  appear  when  the  solution  is  viewed 
through  a  spectroscope.  The  transmitted  light  instead  of  being 
of  the  continuous  spectrum  which  blends  to  subjective  white  is 
made  up  of  the  unaffected  wave  lengths  and  of  those  wave  trains 
the  intensities  of  which  have  been  reduced  to  a  greater  or  lesser 


THEORY   OF   INDICATORS  65 

extent.     The  resultant  subjective  color  must  be  distinguished  from 
the  color  associated  with  a  definite  region  of  the  spectrum. 

We  come  now  to  the  consideration  of  a  phenomenon  which  is 
undoubtedly  exhibited  with  all  indicators  but  which  is  generally 
not  noticed  except  in  special  instances.  In  some  of  these  instances 
it  becomes  of  great  importance  and  may  lead  to  serious  error  unless 
recognized.  The  phenomenon  we  speak  of  is  the  dichromatism 
exhibited,  for  instance,  by  solutions  of  brom  phenol  blue.  Solu- 
tions of  this  indicator  appear  blue  when  viewed  in  thin  layers  but 
red  in  deep  layers.  The  explanation  is  as  follows :  The  dominant 
absorption  band  of  the  alkaline  solution  is  in  the  yellow  and  the 
green,  so  that  the  transmitted  light  is  composed  almost  entirely 
of  the  red  and  blue.  The  incident  light  has  an  intensity  which 
we  may  call  I.  After  transmission  through  unit  thickness  of 
solution  some  of  the  light  has  been  absorbed  and  the  intensity 
becomes  la,  where  a  is  a  fraction — the  transmission  coefficient — 
which  depends  upon  the  nature  of  the  absorbing  medium  and  the 
wave  length  of  the  light.  After  traversing  thickness  e  the  inten- 
sity becomes  Iae.  Now  the  transmitted  blue  is  Ib«b€  and  the 
transmitted  red  Irare.  We  do  not  happen  to  know  what  the 
actual  values  are,  but,  merely  to  illustrate  the  principle,  let  us1 
assume  first  that  the  intensity  of  the  incident  blue  is  100  and  of  the 
red  30  and  that  a^  =  0.5  and  at  =  0.8. 

For  e  =  1,  Ibab*  =  50  and  Irar6  =  24.     Hence  blue  greater  than 
red. 

For'  e  =  10,  Ibflb6  =  0.01  and  Irare  =  0.30.     Hence  blue  less  than 
red. 

This  example  indicates  that  the  solution  may  appear  blue 
when  viewed  through  thin  layers  while  it  may  appear  red  when 
viewed  through  thick  layers. 

If  we  change  the  relative  intensities  of  the  incident  red  and  blue 
we  can  change  the  color  of  a  given  thickness  of  solution.  If  in 
the  above  example  we  reversed  the  intensities  of  the  incident  red 
and  blue,  then, 

For  e  =  1,  Ibflbe  =  15  and  Irar€  =  80,  or  red  greater  than  blue. 

This  is  essentially  what  happens  when  we  carry  the  solution 
•rom  daylight,  rich  in  blue,  to  the  light  of  an  electric  carbon  fila- 


66  THE   DETERMINATION   OF   HYDROGEN   IONS 

ment  lamp,  poor  in  blue.     The  solution  which  appears  blue  in 
daylight  appears  red  in  the  electric  light. 

The  practical  importance  of  recognizing  the  nature  of  this 
phenomenon  may  be  illustrated  in  the  following  way.  Suppose 
we  have  a  solution  rich  in  suspended  material  such  as  bacterial 
cells,  and  that  we  wish  to  determine  its  pH  value  by  using  brom 
phenol  blue.  If  we  view  such  a  solution  in  deep  layers  very  little 
of  the  light  incident  at  the  bottom  reaches  the  eye.  A  large 
proportion  of  the  light  which  does  reach  the  eye  is  that  which 
has  entered  from  the  side,  has  been  reflected  by  the  suspended 
particles,  and  has  traversed  only  a  relatively  thin  section  of  the 
solution.  In  such  a  solution  then,  if  it  is  of  the  proper  pH,  brom 
phenol  blue  will  appear  blue,  while  in  a  clear  comparison  solution 
of  the  same  pH  the  indicator  appears  red  or  purple  if  the  tube  is 
viewed  lengthwise.  A  comparison  is  therefore  impossible  under 
these  conditions.  If,  however,  we  view  the  two  solutions  in  rela- 
tively thin  layers,  as  from  the  side  of  a  test  tube,  they  will  appear 
more  nearly  comparable.  There  will  still  remain,  however,  a 
clearly  recognizable  difference  in  the  quality  of  the  color  which 
serves  as  a  warning  that  the  two  solutions  are  not  being  compared 
under  proper  conditions. 

Now  a  change  in  the  quality  of  the  light  in  which  the  turbid 
and  the  clear  solutions  are  compared  will,  of  course,  not  avert 
one  fundamental  difficulty — a  difference  in  effective  path;  but  a 
proper  change  in  the  quality  of  the  light  can  eliminate  the  di- 
chromatism  and  free  the  eye  from  one  source  of  confusion.  In 
the  case  at  hand  we  might  eliminate  either  the  red  or  the  blue. 
Which  had  best  be  eliminated  is  a  question  which  can  not  be 
answered  properly  until  we  have  before  us  the  necessary  spectro- 
metric  measurements.  Nevertheless  the  following  observations 
made  with  a  small  hand  spectroscope,  and  the  deductions  there- 
from may  prove  to  be  illuminating. 

i  The  chief  absorption  bands  of  brom  phenol  blue  solutions  occur 
in  the  yellow-green  range  and  in  the  blue.  In  alkaline  solutions 
the  band  in  the  blue  disappears  while  that  in  the  yellow  widens 
into  the  green.  As  the  solution  is  made  more  acid  the  band  in 
the  blue  appears,  shutting  off  the  transmitted  blue,  while  that  in 
the  yellow-green  contracts,  permitting  the  passage  of  the  green. 
Our  light  source  then  should  be  such  that  at  least  one  of  these 


THEORY   OF   INDICATORS  67 

changes  may  become  apparent,  and  at  the  same  time  either  the 
blue  or  red  must  be  eliminated.  The  light  of  the  mercury  arc 
fulfills  these  conditions.  It  is  relatively  poor  in  red  and  it  emits 
yellow,  green  and  blue  fines  where  the  shifts  in  the  absorption 
bands  of  brom  phenol  blue  occur.  Since  the  mercury  arc  is  not 
generally  available  we  have  devised  a  light  source  to  fulfill  the 
alternative  condition,  namely,  one  which  will  permit  observation 
of  the  contrasts  due  to  the  shift  in  the  yellow-green  band1  and 
which  at  the  same  time  is  free  from  blue.  Such  a  source  is  found 
in  electric  light  from  which  the  blue  is  screened  by  a  translucent 
paper  painted  with  a  yellow,  acid  solution  of  phenol  red.  One  dis- 
advantage of  such  a  screen  is  that  the  red  transmitted  through 
it  is  so  dominant  that  it  obscures  the  contrasts  which  are  due 
to  the  shifting  of  the  yellow-green  absorption  band.  Nevertheless, 
such  a  screen  has  proved  useful  in  pH  determinations  with  brom 
phenol  blue  and  particularly  useful  with  brom  cresol  purple. 
In  either  case  it  is  most  useful  in  the  more  acid  ranges  covered 
by  these  indicators. 

The  device  consists  of  an  ordinary  box  of  convenient  size  in 
which  are  mounted  three  or  four  large  electric  lights  (e.g.,  30  cp. 
3arbon  filaments).  A  piece  of  "tin"  serves  as  reflector.  The  box 
nay  be  fined  with  asbestos  board.  A  piece  of  glass,  cut  to  fit  the 
Dox,  is  held  in  place  on  one  side  by  the  asbestos  lining  and  on  the 
)ther  by  a  few  tacks.  This  glass  serves  only  to  protect  the  screen 
md  is  not  essential.  The  screen  is  made  from  translucent  paper 
mown  to  draughtsmen  as  "Economy"  tracing  paper.  It  is 
stretched  across  the  open  side  of  the  box  and  painted  with  a 
solution  consisting  of  5  cc.  of  0.6  per  cent  phenol  red  and  5  cc. 
)f  M/5  KH2P04  (stock,  standard  phosphate  solution) .  While  the 
)aper  is  wet  it  is  stretched  and  pinned  to  the  box  with  thumb 
acks.  This  arrangement  may  be  constructed  in  a  very  short 
ime  and  will  be  found  very  helpful  in  many  cases.  It  should  be 
ised  in  a  dark  room  or,  if  such  a  room  is  not  available,  exterior 
ight  may  be  shut  off  with  a  photographer's  black  cloth. 

While  considering  light  sources  we  may  call  attention  to  the 
:  act  that  all  the  sulfon  phthalein  indicators  may  be  used  in  elec- 

1  This  should  not  be  confused  with  the  changes  in  "subjective  color." 
~_  n  the  screened  light  no  participation  of  transmitted  green  will  be  detected 
1  y  the  unaided  eye. 


68  THE  DETERMINATION  OF  HYDROGEN  IONS 

trie  light,  although  brom  thymol  blue  and  thymol  blue  are  not 
well  adapted  for  use  in  light  poor  in  blue.  Doubtless  a  more 
thorough  investigation  of  the  absorption  spectra  of  the  sulfon 
phthalein  indicators  will  make  it  possible  to  devise  light  sources 
which  will  materially  increase  their  efficiency. 

So  far  as  we  have  been  able  to  detect  with  instruments  at  hand, 
the  absorption  spectra  of  all  the  indicators  of  the  sulfon  phthalein 
series  are  such  that  the  appearance  of  dichromatism  must  be 
expected  under  certain  conditions.  It  will  be  observed  with  phe- 
nol red  in  light  relatively  poor  in  red  and  rich  in  blue,  for  example, 
the  light  of  a  mercury  arc;  and  with  thymol  blue  in  light  relatively 
poor  in  blue  and  rich  in  red  for  example,  ordinary  electric  light. 

When  the  colorimeter  is  employed  in  the  study  of  colored  solu- 
tions the  applicability  of  Beer's  law  is  assumed.     This  may  be 

Lii       O2 

expressed  in  the  form,  —  =  —  where  Ci  and  C2  represent  the 

concentrations  of  color  in  two  solutions  and  Li  and  L2  represent 
the  depths  of  solution  traveled  by  the  light  when  a  color  match 
occurs.  Applying  this  relation  one  is  able  to  obtain  the  ratio  of 
concentrations  and  therefrom  the  concentration  in  one  solution 
if  the  concentration  in  the  other  be  known.  But  as  was  shown 
above  we  have,  in  the  case  of  two-color  indicators,  different  trans- 
mission coefficients  for  various  regions  of  the  spectrum.  Conse- 
quently the  depth  of  a  solution  cannot  be  altered  as  it  is  in  the 
ordinary  colorimeter  without  seriously  affecting  the  quality  of  the 
emergent  light. 

When  such  shifts  in  quality  occur  it  is  impossible  without  the 
aid  of  elaborate  photometric  devices  to  make  an  accurate  com- 
parison of  intensities.  This  at  once  limits  the  usefulness  of  the 
ordinary  colorimeter,  a  cardinal  principle  of  which  is  an  accurate 
device  for  varying  and  measuring  the  depth  of  view.  That 
feature  of  certain  instruments  whereby  two  optical  fields  are 
brought  into  juxtaposition  remains  most  useful. 

This  last  and  other  mechanical  features  should  at  once  be  de- 
veloped for  the  colorimeter  devised  by  Gillespie  (1921)  which 
promises  to  be  of  very  great  value  in  exact  indicator  work.  The 
principle  of  Gillespie's  colorimeter  is  shown  in  figure  10.  The 
vessels  A,  B,  C,  D  and  E  are  of  colorless  glass  the  bottoms  of 
which  should  be  optically  polished  plane-parallel.     A  and  C  are 


THEORY   OF   INDICATORS 


69 


fixed  while  B  may  be  moved  up  or  down.  The  position  of  B  is 
indicated  on  a  scale  the  zero  mark  of  which  corresponds  to  the 
position  of  B  when  B  and  C  are  in  contact  and  the  100  mark 
of  which  corresponds  to  the  position  of  B  when  B  is  in  contact 
with  A.  If  now  there  is  placed  in  B  a  solution  of  the  acid  form 
of  an  indicator  and  in  C  a  solution  of  the  same  concentration  of 
the  indicator  transformed  completely  to  the  alkaline  form,  it  is 
obvious  that  the  position  of  the  vessel  B  will  determine  the  ratio 
of  the  two  forms  of  the  indicator  which  will  be  within  the  view. 


*i  A 

B 
C 

D 

E 

Fig.  10.    Diagrammatic  Section  op  Gillespie's  Colorimeter 

For  comparison  studies  a  solution  to  be  tested  is  placed  in  E 
together  with  that  concentration  of  indicator  that  occurs  in  the 
optical  system  B-C.  For  colored  solutions  tubes  A  and  D  are 
used  as  in  the  Walpole  system,  which  will  presently  be  described. 
As  Gillespie  has  indicated  this  colorimeter  should  be  useful  for 
certain  general  work  where  the  exact  principles  of  colorimetry 
have  often  been  neglected. 

There  have  been  two  chief  methods  of  dealing  with  the  interfer- 
ing effect  of  the  natural  color  of  solutions.  The  first  method, 
used  by  S0rensen,  consists  in  coloring  the  standard  comparison 
solutions  until  their  color  matches  that  of  the  solution  to  be  tested, 
md  subsequently  adding  to  each  the  indicator. 


70  THE   DETERMINATION    OP   HYDROGEN   IONS 

S0rensen's  coloring  solutions  are  the  following : 

a.  Bismarck  brown  (0.2  gram  in  1  litre  of  water). 

b.  Helianthin  II  (0.1  gram  in  800  cc.  alcohol,  200  cc.  water). 

c.  Tropeolin  O  (0.2  gram  in  1  litre  of  water). 

d.  Tropeolin  OO  (0.2  gram  in  1  litre  of  water). 

e.  Curcumein  (0.2  gram  in  600  cc.  alcohol,  400  cc.  water). 
/.  Methyl  violet  (0.02  gram  in  1  litre  of  water) . 

g.  Cotton  blue  (0.1  gram  in  1  litre  of  water). 

The  second  method  was  introduced  by  Walpole  (1910).  It  con- 
sists in  superimposing  a  tube  of  the  colored  solution  over  the 
standard  comparison  solution  to  which  the  indicator  is  added, 
and  comparing  this  combination  with  the  tested  solution  plus 
indicator  superimposed  upon  a  tube  of  clear  water. 

A  somewhat  crude  but  nevertheless  helpful  application  of  Wal- 
pole's  principle  may  be  made  from  a  block  of  wood.  Six  deep 
holes  just  large  enough  to  hold  ordinary  test  tubes  are  bored 
parallel  to  one  another  in  pairs.  Adjacent  pairs  are  placed  as 
close  to  one  another  as  can  be  done  without  breaking  through  the 
intervening  walls.  Perpendicular  to  these  holes  and  running 
through  each  pair  are  bored  smaller  holes  through  which  the  test 
tubes  may  be  viewed.  The  center  pair  of  test  tubes  holds  first 
the  solution  to  be  tested  plus  the  indicator  and  second  a  water 
blank.  At  either  side  are  placed  the  standards  colored  with  the 
indicator  and  each  backed  by  a  sample  of  the  solution  under  test. 
This  is  the  so  called  "comparator"  of  Hurwitz,  Meyer,  and 
Ostenberg  (1915).  Before  use  it  is  well  to  paint  the  whole  block 
and  especially  the  holes  a  non-reflecting  black.  To  produce  a 
"dead"  black  use  a  soft  wood  and  an  alcohol  wood-stain.  This 
simple  comparator  is  illustrated  in  figure  7. 

One  or  another  of  the  means  described  serves  fairly  well  in  over- 
coming the  confusing  influence  of  moderate  color  in  solutions  to 
be  tested.  In  bacteriological  work,  however,  a  most  serious  diffi- 
culty is  presented  by  the  suspension  of  cells  and  precipitates. 

If  one  views  lengthwise  a  tube  containing  suspended  particles, 
or  even  particles  of  grosser  colloid  dimensions,  much  of  the  light 
incident  at  the  bottom  is  absorbed  or  reflected  before  it  reaches 
the  eye,  and,  if  the  tube  is  not  screened,  some  of  the  light  which 
reaches  the  eye  is  that  which  has  entered  from  the  side  and  has 
been  scattered.  Consequently,  a  comparison  with  a  clear  standard 
is  inadequate. 


THEORY   OF  INDICATORS  71 

S0rensen  (1909)  has  attempted  to  correct  for  this  effect  by  the 
use  of  a  finely  divided  precipitate  suspended  in  the  comparison 
solution.  This  he  accomplishes  by  forming  a  precipitate  of 
BaS04  through  the  addition  of  chemically  equivalent  quantities 
of  BaCl2  and  Na2S04.  Strictly  speaking,  this  gives  an  imperfect 
imitation,  but  like  the  attempt  to  match  color  it  does  very  well 
in  many  instances.  The  Walpole  superposition  method  may  be 
used  with  turbid  solutions  as  well  as  with  colored,  as  experience 
with  the  device  of  Hurwitz,  Meyer  and  Ostenberg  has  shown.  In 
passing,  attention  should  be  called  to  the  fact  that  the  view  of  a 
turbid  solution  should  be  made  through  a  relatively  thin  layer. 
When  the  comparison  is  made  in  test  tubes,  for  instance,  the  view 
should  be  from  the  side. 

There  are  some  solutions,  however,  which  are  so  dark  or  turbid 
that  they  cannot  be  handled  with  much  precision  by  any  of  these 
methods.  On  the  other'  hand  a  combination  of  these  methods 
with  moderate  and  judicious  dilution  [as  was  indicated  in  Chap- 
ter II  this  may  not  seriously  alter  the  pH  of  a  solution],  permits 
very  good  estimates  with  solutions  which  at  first  may  appear 
impossible.  Some  of  the  deepest  colored  solutions  permit  reason- 
ably good  determinations  "and  when  sufficiently  transparent  per- 
mit the  application  of  spectrometric  devices.  Turbidity  on  the 
other  hand  is  sometimes  unmanageable.  Even  in  the  case  of 
milk  where  comparison  with  a  standard  is  out  of  the  question  a 
two  colored  indicator  presents  a  basis  for  judgment. 

This  brings  us  to  a  phase  of  the  question  the  detailed  analysis 
of  which  will  not  be  attempted.  It  may  simply  be  stated  as  a 
fact  of  experience  that  the  color  change  of  a  two-color  indicator, 
presenting  as  it  does  change  in  intensities  of  what  we  may  sum- 
marily describe  as  two  colors,  is  a  change  in  quality  which  is 
unmistakable  within  narrow  limits.  When  there  is  added  to  this 
that  brilliancy  which  is  characteristic  of  the  sulfon  phthalein 
indicators  the  subjective  aspect  of  indicator  work  is  taken  care 
of  in  a  way  that  may  surprise  one. 

The  spectrophotometer  and  allied  instruments  which  have 
served  in  many  of  the  investigations  of  indicators  have  not  yet 
been  brought  within  the  range  of  ordinary  colorimetric  procedure 
for  the  determination  of  pH.  Where  there  occurs  a  great  change 
in  the  absorption  bands,  as  at  the  endpoint  of  a  titration,  the  hand 


72  THE   DETERMINATION   OF   HYDROGEN   IONS 

spectroscope  may  be  applied  but  it  is  doubtful  if  such  an  instru- 
ment is  of  much  value  for  slight  differences  of  virage.  For  the 
possibilities  which  remain  for  development  in  this  field  the  reader 
is  referred  to  the  special  literature. 

This  brief  sketch  of  some  of  the  principal  aspects  of  indicator 
theory  would  be  incomplete  were  attention  not  called  to  the  value 
of  indicators  for  demonstrating  to  students  important  relations 
among  acids  and  bases.  Indicators  also  call  our  attention  to 
molecular  transformations  which  we  seldom  think  of  as  occurring 
among  substances  the  light  absorptions  of  which  are  in  regions  of 
the  spectrum  beyond  the  reach  of  the  eye. 

And  finally,  indicator  colors  bring  to  the  thoughtful  observer 
their  own  intrinsic  beauty  and  also  reminders  of  how  far  we  have 
come  along  the  road  of  understanding  and  of  how  very,  very  far 
we  still  have  to  go. 


CHAPTER  V 
Choice  of  Indicators 

From  the  enormous  number  of  colored  compounds  found  in 
nature  and  among  the  products  of  the  laboratory  many  have 
been  called  into  use  as  acidimetric-alkalimetric  indicators.  Among 
those  of  plant  origin  litmus  and  alizarine  are  the  more  familiar. 
One  indicator  of  animal  origin,  cochineal,  an  extract  of  an  insect, 
was  formerly  used  to  some  extent.  Walpole's  (1913)  treatment 
of  litmus,  Walbum's  (1913)  study  of  the  coloring  matter  of  the 
red  cabbage  and  some  of  the  more  recent  work,  has  given  us  a 
little  data  on  properties  of  plant  and  animal  pigments  which  are 
applicable  to  hydrogen  ion  determinations.  But  for  the  most 
part  indicators  of  natural  origin  have  been  neglected  for  the  study 
of  synthetic  compounds. 

Litmus  has  played  so  important  a  role  in  acidimetry  that  it  is 
worthy  of  brief,  special  mention. 

Litmus  is  obtained  by  the  oxidation  in  the  presence  of  ammonia 
of  the  orcin  contained  in  lichens,  generally  of  the  species  Roccella 
and  Lecanora.  The  material  which  comes  upon  the  market  is 
frequently  in  the  form  of  cubes  composed  of  gypsum  or  similar 
material  and  comparatively  little  of  the  coloring  matter.  The 
coloring  matter  is  a  complex  from  which  there  have  been  isolated 
many  compounds,  chief  among  which  are  azolitmin,  erythrolitmin, 
erythrolein  and  spaniolitmin.  Of  these  the  azolitmin  is  the  most 
important;  but  the  azolitmin  of  commerce  is  of  uncertain  compo- 
sition, Scheitz  (1910).  The  composition  of  the  different  prepara- 
tions varies  with  the  source  and  also  with  the  extent  of  the  action 
of  alkali  and  air  upon  the  crude  material. 

The  following  method  of  preparing  a  sensitive  litmus  solution 
is  taken  from  Morse  (1905). 

The  crushed  commercial  litmus  is  repeatedly  extracted  with  fresh  quan- 
tities of  85  per  cent  alcohol  for  the  purpose  of  removing  a  violet  coloring 
matter  which  is  colored  by  acids  but  not  made  blue  by  alkalies.  The  resi- 
due, consisting  mainly  of  calcium  carbonate,  carbonates  of  the  alkalies  and 
the  material  to  be  isolated,  is  washed  with  more  hot  alcohol  upon  a  filter 

73 


74  THE   DETERMINATION   OF   HYDROGEN   IONS 

and  then  digested  for  several  hours  with  cold  distilled  water.  The  filtered 
aqueous  extract  has  a  pure  blue  color  and  contains  an  excess  of  alkali,  a 
part  of  which  is  in  the  form  of  carbonate  and  a  part  in  combination  with 
litmus.  To  remove  the  alkaline  reaction  the  solution  is  heated  to  the  boil- 
ing point  and  cautiously  treated  with  very  dilute  sulfuric  acid  until  it  be- 
comes very  distinctly  and  permanently  red.  Boil  till  all  CO2  is  dispelled. 
Treat  with  a  dilute  solution  of  barium  hydroxide  until  the  color  changes  to 
a  violet.  Filter,  evaporate  to  a  small  volume  and  precipitate  the  litmus 
with  strong  alcohol.    Wash  with  alcohol  and  dry. 

Dr.  P.  Rupp  (private  communication)  prefers  to  make  a  final 
washing  with  water  which  removes  much  of  the  salt  at  the  expense 
of  some  dye. 

Synthetic  indicators  have  for  the  most  part  displaced  those  of 
natural  origin  until  litmus  and  alizarine,  turmeric  and  cochineal 
are  becoming  more  and  more  unfamiliar  in  the  chemical  labora- 
tory. Indeed  Bjerrum  (1914)  states  that  the  two  synthetic  indi- 
cators, methyl  red  and  phenolphthalein,  particularly  because  of 
the  zones  of  hydrogen  ion  concentration  within  which  they  change 
color,  are  sufficient  for  most  titrimetric  purposes. 

But  the  two  indicators  mentioned  above  cover  but  a  very  lim- 
ited range  of  hydrogen  ion  concentration  so  that  they  are  insuf- 
ficient for  the  purpose  we  now  have  under  consideration.  A  sur- 
vey of  indicators  suitable  for  hydrogen  ion  determinations  was 
opened  in  Nernst's  laboratory  in  1904  by  Salessky.  This  survey 
was  extended  in  the  same  year  by  Friedenthal,  by  Fels  and  by 
Salm  and  the  results  were  summarized  in  Salm's  famous  table 
(cf.  Z.  physik.  Chem.,  57). 

Then  came  the  classic  work  of  S0rensen  of  the  Carlsberg  lab- 
oratory in  Copenhagen.  The  array  of  available  indicators  had 
become  so  large  as  to  be  burdensome.  S0rensen  in  an  extensive 
investigation  of  the  correspondence  between  colorimetric  and 
electrometric  determinations  of  hydrogen  ion  concentrations  re- 
vealed discrepancies  which  were  attributed  mainly  to  the  influence 
of  protein  and  salts.  He  chose  those  indicators  which  were  rela- 
tively free  from  the  so-called  protein  and  salt  errors,  constructed 
solutions  of  known  and  reproducible  hydrogen  ion  concentra- 
tions and  thus  furnished  the  biochemist  with  selected  tools  of  beau- 
tiful simplicity.  It  is  well  to  emphasize  the  labor  of  elimination 
which  S0rensen  performed  because  without  it  we  might  still  be 
consulting  such  tables  as  that  published  by  Thiel  (1911),  or  the 


CHOICE    OF   INDICATORS  75 

ponderous  tables  8-19,  pages  84-94,  and  be  bewildered  by  the 
very  extensive  array. 

S0rensen's  work,  coupled  as  it  was  with  a  most  important  con- 
tribution to  enzyme  chemistry  gave  great  impetus  to  the  use  of 
indicators  in  biochemistry.  His  selection  of  indicators  was  there- 
fore soon  enlarged  by  additions  of  new  indicators  which  fulfilled 
the  criteria  of  reliability  which  he  had  laid  down.  Alpha  naphthol 
phthalein,  a  compound  first  synthesized  by  Grabowski  (1871), 
was  shown  by  S0rensen  and  Palitzsch  (1910)  to  have  a  range 
of  pH  7-9  and  was  found  useful  in  biological  fluids.  Methyl  red 
(Rupp  and  Loose,  1908)  was  given  its  very  useful  place  by  the 
investigations  of  Palitzsch  (1911).  Henderson  and  Forbes  (1910) 
introduced  2-5  di  nitro  hydroquinone  as  an  indicator  possessing 
several  steps  of  color  change  and  therefore  useful  over  a  wide  range 
of  pH.  Walpole  (1914)  called  attention  to  several  indicators  of 
potential  value.  Hottinger  (1914)  recommended  "lacmosol," 
a  constituent  of  lacmoid,  and  Scatchard  and  Bogert  (1916) 
advocated  the  use  of  dinitro  benzoylene  urea.  There  remain  a 
host  of  indicators  which  have  been  tried  out  in  the  empirical 
practices  of  titration  but  which  have  never  had  their  pH  ranges 
determined ;  and  there  remain  an  unlimited  number  of  possibilities 
embodied  in  existing  compounds  such  as  Dox's  (1915)  phenol 
quinolinein,  Rupp's  (1915)  syntheses  in  the  methyl  red  series 
and  untouched  homologues  of  phenol  phthalein  and  of  phenol 
sulfon  phthalein.  Furthermore,  there  undoubtedly  are  still 
unsynthesized  compounds  of  various  types,  old  and  new,  which 
will  some  day  displace  those  now  in  use. 

In  1915  Levy,  Rowhtree  and  Marriott,  without  applying  the 
tests  of  reliability  which  S0rensen  had  employed,  used  phenol 
sulphon  phthalein  in  determining  the  pH  of  the  dialyzate  of  blood. 
This  compound,  first  synthesized  in  Remsen's  laboratory  by  Sohon 
(1898),  has  received  considerable  attention  from  Acree  and  his 
co-workers  because  it  furnishes  excellent  material  for  the  quinone- 
phenolate  theory  of  indicators.  To  further  such  studies  Acree 
and  White  had  synthesized  new  derivatives  of  phenol  sulphon 
phthalein  at  the  time  when  the  work  of  Levy,  Rowntree  and 
Marriott  attracted  the  attention  of  Clark  and  Lubs.  These  authors 
.  were  looking  for  more  brilliant  indicators  for  use  in  bacterial  cul- 
ture media  and  were  attracted  by  the  well  known  brilliance  of 


76  THE  DETERMINATION  OF  HYDROGEN  IONS 

phenol  sulphon  phthalein.  Through  the  courtesy  of  Professor 
Acree  some  of  the  derivatives  which  White  had  prepared  were 
obtained.  New  homologues  were  synthesized  by  Lubs.  The 
applicability  of  these  and  numerous  other  indicators  in  the  deter- 
mination of  the  pH  values  of  biological  fluids  was  then  studied. 

In  the  sulfon  phthalein  series  the  following  were  studied: 

Phenol  sulfon  phthalein,  Sohon  (1898). 

Tetra  nitro  phenol  sulfon  phthalein,  White  and  Acree  (1915). 

Phenol  nitro  sulfon  phthalein,  Lubs  and  Clark  (1915). 

Tetra  bromo  phenol  sulfon  phthalein,  White  and  Acree  (1915). 

Tetra  chloro  phenol  sulfon  phthalein,  Lubs  and  Clark. 

Ortho  cresol  sulfon  phthalein,  Sohon  (1898). 

Di  bromo  ortho  cresol  sulfon  phthalein,  Sohon  (1898). 

Thymol  sulfon  phthalein,  Lubs  and  Clark  (1915). 

Thymol  nitro  sulfon  phthalein,  Lubs  and  Clark. 

Di  bromo  thymol  sulfon  phthalein,  Lubs  and  Clark  (1915). 

a-napthol  sulfon  phthalein,  Lubs  and  Clark  (1915). 

Carvacrol  sulfon  phthalein,  Lubs  and  Clark. 

Orcinol  sulfon  phthalein,  Gilpin  (1894). 

The  attractiveness  of  methyl  red  led  to  the  study  of  the  fol- 
lowing compounds : 

o-carboxy  benzene  azo  mono  methyl  aniline,  Sive  and  Jones 
(1915). 

o-carboxy  benzene  azo  di   methyl   aniline,    Rupp   and   Loose 
(1908). 

o-carboxy  benzene  azo  mono  ethyl  aniline,  Lubs  and  Clark 
(1915). 

o-carboxy  benzene  azo  di  ethyl  aniline,  Lubs  and  Clark  (1915). 

o-carboxy  benzene  azo  mono  propyl  aniline,  Lubs  and  Clark 
(1915). 

o-carboxy  benzene  azo  di  propyl  aniline,  Lubs  and  Clark  (1915). 

o-carboxy  benzene  azo  (?)  amyl  aniline,  Lubs  and  Clark  (1915). 

o-carboxy  benzene  azo  di  methyl  a  naphthyl  amine,  Howard 
and  Pope  (1911). 

o-carboxy  benzene  azo  a  naphthyl  amine,  Howard  and  Pope 
(1911). 

o-carboxy  benzene  azo  di  phenyl  amine,  Howard  and  Pope 
(1911). 

Meta  carboxy  benzene  azo  di  methyl  aniline,  Lubs  and  Clark. 


CHOICE   OF  INDICATORS  77 

The  mono  alkyl  homologues  of  methyl  red  were  found  to  be 
much  less  brilliant  than  the  di  alkyl  compounds  and  were  there- 
fore rejected.  For  the  same  reason  or  because  of  large  protein 
errors  we  rejected  the  other  compounds  with  the  exception  of 
di  ethyl  and  di  propyl  red.  Of  these  we  retained  di  propyl  red 
because  it  is  very  useful  in  solutions  of  a  little  lower  hydrogen  ion 
concentration  than  those  which  may  be  studied  with  methyl  red. 

Propyl  red  is,  however,  not  included  in  table  6  because  it 
precipitates  too  easily  from  buffer  solutions  to  be  of  general 
usefulness. 

As  the  result  of  an  extensive  series  of  comparisons  between 
colorimetric  and  electrometric  measurements,  made  for  the  most 
part  upon  solutions  of  interest  to  bacteriologists,  Clark  and  Lubs 
(1917)  suggested  the  series  of  indicators  given  in  table  6.  This 
series  is  made  up  for  the  most  part  of  the  brilliant  and  more 
reliable  sulfon  phthaleins  but  contains  the  still  indispensable  but 
not  very  stable  methyl  red. 

In  the  course  of  their  investigations  these  authors  resurrected 
ortho  cresol  phthalein  (Baeyer  and  Freude,  1880),  found  it  quite 
as  reliable  as  phenolphthalein  and  more  brilliant  with  a  color 
better  adapted  to  titrations  in  artificial  light. 

In  spite  of  the  fact  that  S0rensen  rejected  the  greater  number 
of  the  indicators  which  he  studied  and  that  Clark  and  Lubs,  after 
a  resurvey  of  the  subject  and  the  preparation  of  many  new  com- 
pounds, listed  but  few  indicators  as  reliable,  there  has  recently 
appeared  a  tendency  to  resurrect  the  rejects.  Now  many  of 
these  are  useful  in  special  cases  and  undoubtedly  there  is  an 
occasional  individual  to  be  found  in  the  lists  which  has  been 
insufficiently  studied  and  unjustly  rejected.  Nevertheless,  the 
indiscriminate  use  of  miscellaneous  indicators  may  lead  to  gross 
errors  or  at  least  to  such  a  diversity  of  data  that  their  correlation 
will  become  complex  during  the  coming  period  when  the  Specific 
salt-errors  and  general  conduct  of  the  individual  indicators  are 
still  being  worked  up. 

It  is  therefore  advisable  to  use  the  more  thoroughly  studied 
lists.  Three  such  lists  are  given  (tables  5,  6  and  7).  The  indi- 
cators therein  listed  should  cover  all  ordinary  needs.  S0rensen's 
list  is  given  in  table  5  and  to  this  is  appended  S0rensen's 
comments.     For  general  purposes  the  selection  of  indicators  given 


78 


THE  DETERMINATION  OF  HYDROGEN  IONS 


in  table  6  will  be  found  the  most  satisfactory  especially  because 
of  their  brilliancy.  Each  of  these  however  has  its  own  special 
limitations  as  every  indicator  has.  For  the  study  of  colorless 
solutions  where  salt  errors  are  to  be  reduced  the  nitro  phenols 
listed  in  table  7  should  be  valuable. 

TABLE  5 

Sfirenseri's  selected  indicators 

Figures  in  parentheses  refer  to  Schultz  (1914).     Figures  1-20  are  S0rensen's 


INDICATOR 


10. 
11. 

12. 
18. 

14. 
15. 
16. 
17. 

18. 
10. 

20. 


Methyl  violet  6B  extra,  (517) 

Mauvein,  Rosolane,  (688) 

Diphenylamino-azo-benzene 

Diphenylamino-azo-p-benzene  sulfonic  acid,  Tro- 
paeolin  00,  (139) 

Diphenylamino-azo-m-benzene  sulfonic  acid,  Metanil 
yellow,  (134) 

Benzyl  anilino-azo-benzene 

Benzylanilino-azo-p-benzene  sulfonic  acid 

Metachloro  diethyl-anilino-azo-p-benzene  sulfonic 
acid 

Dimethyl  anilino-azo-benzene,  (32) 

Methyl  orange,  Helianthine,  (138) 

a  naphthylamino-azo-benzene 

a-naphthylamino-azo-p-benzene  sulfonic  acid 

Para  nitro  phenol 

Neutral  red,  (670) 

Rosolic  acid,  Aurin,  (555) 

Orange  I,  Tropaeolin  000  No.  1,  (144) 

Phenolphthalein. 

Thymolphthalein 

Paranitrobenzene-azo-salicylic  acid,  Alizarine  yel- 
low R,  (58) 

Resorcin-azo-p-benzene  sulfonic  acid,  Tropaeolin  0, 
(143) 


pH  RANGE 

0.1- 

3.2 

0.1- 

2.9 

1.2- 

2.1 

1.4- 

2.6 

1.2- 

2.3 

2.3- 

3.3 

1.9-  3.3 

2.6- 

4.0 

2.9-  4.0 

3.1- 

4.4 

3.7- 

5.0 

3.5- 

5.7 

5.0-  7.0 

6.8- 

8.0 

6.8- 

8.0 

7.6-  8.9 

8.3- 

10.0 

9.3- 

10.5 

10.1- 

12.1 

11.1- 

12.7 

In  tables  8-20  are  a  few  indicators  which  are  undoubtedly 
reliable  but  little  used,  a  few  which  are  definitely  unreliable 
though  often  used,  and  very  many  of  uncertain  character  but 
for  the  most  part  bearing  the  stamp  of  disapproval  by  competent 
judges.  Since  the  indicators  in  tables  5,  6  and  7  cover  all  ordinary 
requirements  it  seems  hardly  worth  while  to  venture  upon  an 
analysis  of  the  remaining  tables. 


CHOICE    OF   INDICATORS  79 

In  table  5  is  S^rensen's  list  of  indicators;  concerning  these  indicators 
S0rensen  remarks: 

Not  all  these  indicators  furnish  equally  well  defined  virages  and  above 
all  they  are  not  of  equal  applicability  under  all  circumstances.  In  the 
choice  of  an  indicator  from  among  those  which  we  have  been  led  to  recom- 
mend it  is  necessary  to  use  judicious  care  and  especially  to  take  into  con- 
sideration the  following  facts: 

a.  The  indicators  of  the  methyl  violet  group  (nos.  1  and  2)  (see  table  5) 
are  especially  sensitive  to  the  action  of  neutral  salts;  furthermore  the  in- 
tensity of  color  changes  on  standing  and  the  change  is  the  more  rapid  the 
more  acid  the  medium. 

b.  The  basic  indicators  (nos.  3,  6,  9,  11,  14)  are  soluble  in  toluene  and  in 
chloroform.  The  first  four  separate  partially  on  prolonged  standing  of 
the  experimental  solution. 

c.  In  the  presence  of  high  percentages  of  natural  proteins  most  of  the  in- 
dicators are  useless  although  certain  of  them  are  still  serviceable;  nos.  1,  2, 
13,  16,  17,  18. 

d.  In  the  presence  of  protein  decomposition  products  even  in  consid- 
erable proportions  the  entire  series  of  indicators  may  render  real  service. 
Yet  even  in  these  conditions  some  of  the  acid  azo  indicators  may  give 
notable  errors  (nos.  4,  5,  7,  8,  10)  in  which  case  one  should  resort  to  the  cor- 
responding basic  indicators. 

e.  When  only  small  percentages  of  protein  or  their  decomposition  prod- 
ucts are  concerned  the  acid  azo  indicators  are  more  often  preferable  to 
the  basic  for  they  are  not  influenced  by  toluene  or  chloroform  and  do  not 
separate  from  solution  on  standing. 

/.  In  all  doubtful  cases — for  example  in. the  colorimetric  measurement 
of  solutions  whose  manner  of  reaction  with  the  indicator  is  not  known,  the 
electrometric  measurement  as  a  standard  method  should  be  used.  Then 
the  worth  of  the  indicator  will  be  determined  by  electrometric  measurement 
with  colorimetric  comparison. 

In  table  6  will  be  found  the  final  selection  of  Clark  and  Lubs 
with  the  common  names  which  they  suggested  for  laboratory  par- 
lance, the  concentration  of  indicator  convenient  for  use,  a  rough 
indication  of  the  nature  of  the  color,  and  the  useful  pH  range. 

With  the  improved  method  for  the  preparation  of  the  sulfon 
phthalein  indicators  described  by  Lubs  and  Clark  (1915)  they  may 
easily  be  made  from  materials  readily  obtained.  The  indicators 
can  also  now  be  purchased  in  this  country  and  abroad  from 
chemical  supply  houses. 

The  indicators  recommended  by  Clark  and  Lubs  are  marketed 
both  in  the  form  of  a  dry  powder  and  in  stock  solutions.  In  cases 
where  the  acidity  of  the  free  acid  dye  in  the  indicator  solution 


80 


THE  DETERMINATION  OF  HYDROGEN  IONS 


does  not  interfere  with  accuracy  and  when  alcohol  is  not  objec- 
tionable the  alcoholic  solutions  of  the  dyes  may  be  used.  Clark 
and  Lubs  prefer  to  use  aqueous  solutions  of  the  alkali  salts  in 
concentrations  which  may  be  conveniently  kept  as  stock  solu- 
tions. These  are  diluted  for  the  test  solutions  used  in  the  drop- 
ping bottles. 

TABLE  6 
Clark  and  Lubs'  list  of  indicators 


CHEMICAL   NAME 

COMMON   NAME 

S5 
I    0 

B  < 
o 

COLOR  CHANGE 

RANGE 

PH 

Thymol    sulfon 
phthalein  (acid 
range) 

Thymol  blue  (see 
below) 

Brom  phenol  blue 

Methyl  red 

Brom  cresol  pur- 
ple 

Brom  thymol  blue 

Phenol  red 

Cresol  red 

Thymol  blue 

Cresol  phthalein 

per  cent 

0.04 

0.04 

0.02 

0.04 

0.04 
0.02 
0.02 
0.04 
0.02 

Red-yellow 

Yellow-blue 

Red-yellow 

Yellow-purple 

Yellow-blue 

Yellow-red 

Yellow-red 

Yellow-blue 

Colorless-red 

1.2-2.8 

Tetra  bromo  phenol 
sulfon  phthalein 

Ortho  carboxy  ben- 
zene azo  di  methyl 
aniline 

3.0-4.6 
4.4-6.0 

Di  bromo  ortho  cre- 
sol  sulfon  phthal- 
ein  

5.2-6.8 

Di     bromo     thymol 
sulfon  phthalein 

Phenol  sulfon  phthal- 
ein   

6.0-7.6 
6.8-8.4 

Ortho   cresol   sulfon 
phthalein 

7.2-8.8 

Thymol   sulfon 
phthalein 

8.0-9.6 

Ortho  cresol  phthal- 
ein   

8.2-9*8 

For  the  preparation  of  these  stock  solutions  one  decigram  (0.1 
gram)  of  the  dry  powder  is  ground  in  an  agate  mortar  with  the 
following  quantities  of  N/20  NaOH.  When  solution  is  complete 
dilute  to  25  cc.  with  water. 


CHOICE   OF   INDICATORS 


81 


MOLECULAR  WEIGHT 

INDICATOR 

N/20  NaOH  per 

DECIGRAM 

354 
669 
382 
540 
466 
624 
269 

Phenol  red 
Brom  phenol  blue 
Cresol  red 
Brom  cresol  purple 
Thymol  blue 
Brom  thymol  blue 
Methyl  red 

CC. 

5.7 
3.0 
5.3 
3.7 
4.3 
3.2 
7.4 

If  there  be  no  particular  reason  to  maintain  exact  equivalents 
it  may  be  found  easier  to  dissolve  the  dyes  in  1.1  equivalents  of 
alkali  instead  of  one  -equivalent  as  indicated  above. 

When  made  up  to  25  cc.  as  noted  above  there  is  obtained  in 
each  case  a  0.4  per  cent  solution  of  the  original  dye  itself.  For 
tests  they  should  be  diluted  further.  To  place  the  dyes  upon  a 
comparable  basis  the  final  dilution  should  be  nearly  the  same  when 
calculated  upon  a  molar  basis  and,  by  reason  of  the  great  change  in 
molecular  weight  caused  by  the  introduction  of  bromine  and  other 
group  substituents,  equal  molecular  concentrations  will  be  very 
far  apart  in  percentage  concentration.  For  all  ordinary  pur- 
poses, however,  this  may  be  neglected  and  the  solutions  mentioned 
above  if  diluted  in  each  case  to  a  concentration  of  0.04  per 
cent  will  be  found  satisfactory  for  use  in  testing  10  cc.  of  a  solu- 
tion with  about  five  drops  of  indicator. 

From  various  sources  have  come  complaints  that  the  method 
outlined  above  for  the  preparation  of  the  aqueous  alkali  salt 
solution  of  brom  cresol  purple  leads  to  a  solution  of  much  lower 
tinctorial  power  than  when  the  same  material  is  taken  up  directly 
in  alcohol.  No  such  difficulty  was  experienced  with  the  material 
described  by  Lubs  and  Clark  but  it  has  appeared  not  infrequently 
since.  The  source  of  the  difficulty  is  not  yet  definitely  traced, 
but  is  suspected  to  be  due  to  impurities.  If  so  it  should  be 
avoided  by  purchasing  the  highly  purified  material  which  is  now 
made  specially. 

While  the  aqueous  alkali  salt  solution  of  methyl  red  is  preferred 
for  some  purposes  a  methyl  red  solution  can  be  more  conveniently 
prepared  by  dissolving  1  decigram  in  100  cc.  alcohol  and  diluting 
to  200  with  distilled  water. 


82  THE   DETERMINATION    OF   HYDROGEN   IONS 

Ortho  cresol  phthalein  and  phenol  phthalein  are  used  in  a 
0.04  per  cent  solution  of  95  per  cent  alcohol. 

Methyl  red  and  brom  cresol  purple  may  be  recrystallized  from 
hot  toluol,  cresol  red  and  brom  phenol  blue  from  glacial  acetic 
acid,  thymol  blue  from  hot  alcohol. 

Tables  8-20  have  been  compiled  with  the  aid  of  Dr.  Barnett 
Cohen  and  Dr.  Elias  Elvove  with  several  purposes  in  view.  In 
the  first  place  there  exist  in  the  older  literature  a  great  many 
observations  recorded  in  terms  of  the  color  of  a  given  indicator. 
These  data  can  often  be  translated  into  modern  terms  if  the  pH 
range  of  the  given  indicator  is  known.     In  the  second  place  there 

TABLE  7 

Michaelis'  indicators  and  their  ranges  as  used  in  the  method  of  Michaelis  and 

Gyemant  (see  Chapter  VIII) 

Picric  acid colorless  0.0-  1.3  yellow 

2,  4-dinitro  phenol colorless  2.0-  4.7  yellow 

a  dinitro  phenol 

2,  6-dinitro  phenol colorless  1.7-  4.4  yellow 

/3  dinitro  phenol 

2,  5-dinitro  phenol colorless  4.0-  6.0  yellow 

y-dinitro  phenol 

m-nitro  phenol colorless  6.3-  9.0  yellow 

p-nitro  phenol colorless  4.7-  7.9  yellow 

Phenolphthalein colorless  8.5-10.5  red 

Alizarine  yellow  GG colorless  10.0-12.0  yellow 

Salicyl  yellow 

are  circumstances  when  for  one  reason  or  another  it  becomes 
necessary  to  draw  upon  the  miscellaneous  list.  It  should  there- 
fore be  available.  Lastly,  and  perhaps  most  important,  our  review 
of  the  literature  and  of  indicator  labeling  has  shown  that  there 
is  great  confusion  and  an  initial  step  in  the  clarification  of  the 
subject  will  be  taken  if  there  is  available  a  tabulation  of  existing 
data  to  serve  as  a  basis  for  revision. 

In  examining  a  large  collection  of  indicators  the  labeling 
was  found  to  be  insufficient  in  a  large  percentage  of  cases.  On 
studying  the  literature  we  find  evidence  that  others  have 
encountered  the  same  difficulty  without  stating  so,  for  in 
many  instances  the  indicator  names  given  were  evidently  those 


CHOICE    OF   INDICATORS  83 

of  one  or  another  dealer  who  cared  so  little  for  the  scientific  uses 
of  his  commodity  that  he  left  from  the  label  the  designation 
essential  to  its  identification.  This  habit  has  become  more  or  less 
prevalent.  In  some  instances  our  own  uncertainty  may  be  due 
to  an  arbitrary  adherence  to  the  nomenclature  found  in  various 
editions  of  Schultz.  For  instance  when  we  see  the  indicator 
crocei'ne  listed  and  refer  to  Schultz  (1914)  we  find  four  crocei'nes 
with  various  distinguishing  marks  and  seven  other  compounds 
for  the  names  of  which  "croceme"  is  used  in  one  or  another  com- 
bination. But  Schultz  lists  no  croceme.  We  are  not  helped  in  going 
back  to  the  lists  of  Schultz  and  Julius  (1902).  Now  we  might 
assume  that  "croceme"  was  used  in  Salm's  table  as  a  term  having 
a  definite  meaning  outside  the  dye  industry.  On  this  principle 
we  should  find  that  "helianthine"  has  been  employed  in  accordance 
with  scientific  usage.  However  we  find  that  an  old  sample  of 
helianthine  from  Salm's  dealer  is  not  the  helianthine  of  methyl 
orange  but  corresponds  in  pH-range  to  Salm's  Helianthine  I, 
which,  together  with  Salm's  Helianthine  II  we  have  not  identified. 

Again  there  are  other  difficulties  such  as  are  illustrated  by  the 
case  of  Tropaeolin  OOO  No.  1  and  Tropaeolin  000  No.  2.  No.  1 
is  prepared  from  p-sulfanilic  acid  and  a-naphthol.  No  2  is  pre- 
pared from  p-sulfanilic  acid  and  (3-naphthol.  In  this  there  is 
agreement  by  Schultz  and  Julius  1902,  Green  1904  and  Beilstein 
(third  edition).  In  accord  with  this  S0rensen  describes  his 
a-naphthol  preparation  as  Tropaeolin  000  No.  1.  In  the  second 
edition  of  Indicators  and  Test  Papers,  Cohn  (1914)  has  given 
synonyms  for  the  a  and  /3  compounds  which  agree  with  Green, 
but  has  reversed  the  No.  1  and  No.  2  at  the  headings  of  his  de- 
scriptions and  uses  "No.  1"  and  "No.  2"  inconsistently  in  the 
text.  Prideaux  (1917)  has  called  the  /3  compound  Tropaeolin 
000  and  gives  the  range  as  7.6-8.9,  which  looks  suspiciously  like 
S0rensen's  7.6-8.9  for  the  a  compound.  Prideaux  uses  the 
synonym.  Orange  II  for  the  /3  compound  in  .harmony  with  Green 
but  on  the  next  page  describes  the  a  compound  as  Orange  II. 
The  identity  of  Salm's  Tropaeolin  000  is  not  clear.  It  was 
evidently  different  from  the  Tropaeolin  000  No.  1  used  by 
S0rensen.  We  find  that  an  old  sample  with  the  label  "Tro- 
paeolin 000"  agrees  with  neither  S0rensen's  nor  Salm's  data. 

Many  other  instances  might  be  cited  to  show  the  confused 


84 


THE  DETERMINATION  OF  HYDROGEN  IONS 


state  of  the  subject.  Because  it  is  serious  the  reader  will  have 
to  use  the  following  tables  with  caution,  and  he  need  not  be 
surprised  if  a  sample  of  indicator  which  he  tests  does  not  give 
a  pH  range  corresponding  to  that  recorded. 

In  the  compilation  of  the  lists  we  have  followed  competent 
advice  in  using  the  nomenclature  of  Farbstofftabellen,   Gustav 

TABLE  8 
Nitro  compounds 


SERIAL 
NUM- 
BER 

INDICATOR 

pH  RANGE 

1 

Picric  acid  (5) 

colorless 

colorless 
light  yellow 

colorless 

colorless 

colorless 

pink 

colorless 
colorless 
colorless 
colorless 

colorless 
pink 

0.0-  1.3  yellow 

1.7-  4.4  yellow 
2.0-  4.0  yellow 

2.0-  4.7  yellow 
3.0-  9.0  various 
colors 
3.9-  5.9  yellow 

4.0-  6.0  yellow 

4.1—  5.6  yellow 

2 
3 

2,  4,  6-trinitro-phenol 

2,  6-Dinitro-phenol  (fi) 

Martius  yellow  (6) 

4 
5 

6 

7 
8 

2,  4-dinitro-a-naphthol 

2,  4-Dinitro-phenol  (a) 

2,  5-Dinitro-hydroquinone 

2,  3-Dinitro-phenol  (e) 

2,  5-Dinitro-phenol  (7) 

iso-Picramic  acid 

9 
10 

2,  6-dinitro-4-amino- 
phenol 

3,  4-Dinitro-phenol  (5) 

p-Nitro-phenol 

4.3-  6.3  yellow 
5.0-  7.0  yellow 

11 
12 

Dinitrobenzoylene-urea .. . . 

m-Nitro-phenol 

6.0-  8.0  yellow 
6.3-  9.0  yellow 

13 

Nitramine  (?) 

11.0-12.5 

14 
15 

1,  3,  5-Trinitro-benzene 

2,  4,  6-Trinitro-toluene  (TNT) 

11.5-14.0  orange 
11.5-14.0  orange 

Schultz,  fifth  revised  edition,  Berlin,  1914.  In  a  few  cases  there 
have  been  added  to  the  synonyms  in  table  20  terms  which  are 
obsolete  in  the  dye  industry  but  which  are  still  used  in  the  nomen- 
clature of  indicators.  Schultz  numbers  are  to  be  found  in  tables  8 
to  19  following  the  name  of  each  indicator  when  the  given  indi- 
cator is  listed  by  Schultz.  Since  it  is  unimportant  for  indicator 
work,  no  distinction  has  been  made  between  acids  and  their  salts. 
The  classification  by  structure  follows  in  the  main  that  of  Schultz. 


CHOICE   OF  INDICATORS 


85 


TABLE  9 
Monoazo  compounds 


SERIAL 

NUM- 

INDICATOR 

pH  RANGE 

,BER 

16 

Curcumein  (?) 

orange 

0.0-  1.0  yellow, 

yellow    13- 

15  green 

17 

o-Carboxybenzene-azo-(di  or 

mono?)  amyl-aniline . . . 

purple 

0.0-  1.6  orange    (fluo- 
rescent), 
orange  5.6- 
7.6  yellow 

18 

o-Carboxybenzene-azo-m- 

yellow 

0.0-  4.6  orange, 

orange  4.6- 
7.6  yellow 

19 

p-Toluene-az  o-pheny  1-aniline . 

1.0-  2.0 

20 

p-Carboxybenzene-azo-di- 
methyl-aniline    (Para 

methyl  red) 

red 

1.0-  3.0  yellow 

21 

p-Toluene-azo-pbenyl-a-naph- 

thylamine 

1.1-  1.9 

22 

Benzene-azo-diphenylamine. . 

1.2-  2.1 

23 

Metanil  yellow  extra  (134).... 
m-sulfobenzene-azo-di- 
phenylamine 

red 

1.2-2.3  yellow 

24 

Benzene-az  o-pheny  1-a-n  aph- 

thylamine 

1.4-  2.6 

25 

Orange  IV  (139) 

pink 

1.4-  2.6  yellow 

p-sulfobenzene-azo-di- 

phenylamine 

26 

o-Toluene-azo-o-toluidine. . . . 

1.4-  2.9 

27 

p-Toluene-azo-benzyl-a- 

naphthylamine 

1.6-  2.6 

•    28 

p-Toluene-azo-benzyl-aniline. 

1.6-  2.8 

29 

Benzene-azo-benzyl-a-naph- 

1.9-  2.9 

30 

light  yellow 

1.9-  3.3  yellow 

31 

p-Benzenesulfonic    acid-azo- 

aniline 

1.9-  3.3 

32 

p-Benzenesulfonic    acid-azo- 

benzyl-aniline 

1.9-  3.3 

33 

m-Carboxybenzene-azo-di- 

methylaniline 

red 

2.0-  4.0  yellow 
2.3-  3.3 

34 

Benzene-azo-benzyl-aniline.. . 

86 


THE   DETERMINATION 
TABLE  9- 


OF   HYDROGEN   IONS 

Continued 


SERIAL 

NUM- 

INDICATOR 

pH  RANGE 

BER 

35 

p-Benzenesulfonic    acid-azo- 
metachloro-dimethyl- 

aniline 

2.6-  4.0 

36 

Orange  III  (47) 

red 

2.6-  4.6  yellow 

m-nitrobenzene-azo-/3- 

naphthol-3,    6-disulfo- 

nic  acid 

37 

Butter  yellow  0  (32) 

red 

2.9-  4.0  yellow 

benzene-azo-dimethyl- 

aniline 

38 

o-Carboxybenzene-azo-di- 

phenylamine 

pink 

3.0-  4.6  yellow, 

purple    0.0- 

1.6  pink 

39 

p-Benzenesulfonic    acid-azo- 

methyl-aniline 

3.1-  4.2 

40 

p-Benzenesulfonic    acid-azo- 

ethyl-aniline 

3.1-  4.4 

41 

Methyl  orange  (138) 

orange  red 

3.1-  4.4  yellow 

p-benzenesulfonic  acid- 

az  o-dimethy  1-aniline 

42 

p-Benzenesulfonic    acid-azo- 
diethyl-aniline  (Ethyl 

orange) 

pink 

3.5-  4.5  yellow 

43 

p-Benzenesulfonic    acid-azo- 

a-naphthylamine 

3.5-  5.7 

44 

Benzene-azo-a-naphthyl- 

amine 

3.7-  5.0 

45 

p-Toluene-azo-a-naph- 

thylamine 

3.7-  5.0 

46 

o-Carboxybenzene-azo-mono- 

methylaniline 

red 

4.0-  6.0  yellow 

47 

Chrysoidin  (33) 

orange 

4.0-  7.0  yellow 

benzene-azo-m-phenyl- 

enediamine 

48 

o-Carboxybenzene-azo-mono- 

ethylaniline 

red 

4.2-  6.2  yellow 

49 

o-Carboxybenzene-azo-mono- 

n-propylaniline 

red 

4.2-  6.2  yellow 

50 

o-Carboxybenzene-azo-di- 

methylaniline  (Methyl 

red) 

red 

4.2-  6.3  yellow 

51 

o-Carboxybenzene-azo-di- 

ethvlaniline 

red 

4.4-  6.2  yellow 

'        J  v 

CHOICE   OF  INDICATORS 
TABLE  9— Concluded 


87 


1ERIAL 

NUM- 

INDICATOR 

pH  RANGE 

BER 

52 

o-Carboxybenzene-azo-di-n- 
propylaniline  (Propyl 

red) 

red    4.6-  6.6  yellow 

53 

Benzene-azo-dimethyl-a- 

naphthylamine 

4.8-  5.5 

54 

p-Benzenesulfonic    acid-azo- 
dimethyl-a-naph- 

thylamine 

5.0-  5.7 

55 

o-Carboxybenzene-azo-a- 

naphthylamine 

pink   5.6-  7.0  yellow 

56 

o-Carboxybenzene-azo-di- 
methyl-a-naphthyl- 

amine 

red    5.6-  7.6  orange 

57 

Naphthylamine  brown  (160) . . 
4-sulf  onaphthalene-az  o- 
a-naphthol 

orange    6.0-  8.4  pink 

58 

6-Sulf  o-a-naphthol-1-az  o-m- 

hydroxybenzoic  acid . . . 

orange    7.0-  8.0  blue, 

violet  12- 
13  red 

59 

Orange  I  (144) 

7.6-  8.9 

p-sulfobenzene-azo-a- 

naphthol 

60 

Orange  II  (145) 

7.6-  8.9  (?) 

p-sulfobenzene-azo-/S- 

naphthol 

61 

Alizarine  yellow  GG  (48) 
m-nitrobenzene-azo-sali- 
cylic  acid 

colorless  10.0-12.0  yellow 

62 

Alizarine  yellow  R  (58) 

p-nitrobenzene-azo-sali- 
cylic  acid 

pale  yellow  10.1-12.1  orange  . 

63 

Fast  red  A  (161) 

10.5-12.1 

5-sulfonaphthalene-azo- 

/3-naphthol 

64 

Fast  red  B  (112) 

pink  10.5-12.5  orange 

a-naphthalene-azo-/8- 

naphthol-3,    6-disulfo- 

nic  acid 

55 

Chrysoin  (143) 

p-sulfobenzene-azo- 
resorcin 

yellow  11.1-12.7  orange 

36 

Orange  G  (38) 

yellow  11.5-14.0  pink 

benzene-azo-/8-naphthol- 

7-disulfonic  acid 

88 


THE    DETERMINATION   OF   HYDROGEN   IONS 


TABLE  10 
Disazo  compounds 


SERIAL 

NUM- 

INDICATOR 

pH  RANGE 

BER 

67 

Benzopurpurin  B  (365) 

blue-0.3-  1.0  violet, 

ditolyl-disazo-bi-/3-naph- 

violet  1.0- 

thylamine-/3-sulfonic 

5.0  yellow, 

acid 

yellow  12.0- 
14.0  rose 

68 

Congo  (307) 

blue    3.0-  5.0  red 

diphenyl-disazo-binaph- 

thionic  acid 

69 

Azo  blue  (377) 

violet  10.5-11.5  pink 

ditoly  1-disaz  o-bi-a-n  aph- 

thol-4-sulfonic  acid 

TABLE  11 
Triphenylmethane  compounds 


SERIAL 

NUM- 

INDICATOR 

pH  RANGE 

BER 

70 

Crystal  violet  (516) 

green 

0.0-  2.0  blue 

hexamethyl  pararo- 

saniline 

71 

Malachite  green  (495) 

yellow 

0.0-  2.0  green, 

tetramethyl-di-p-amino- 

blue  11.5- 

triphenyl-carbinol 

14.0  fades 

72 

Red  violet  5R  extra  (514) 

mixture  of  mono-,  di-  and 
tri-methyl  or  ethyl  ro- 
sanilines   and    pararo- 
sanilines 

green 

0.0-  2.0  blue 

73 

Brilliant  green  (499) 

yellow 

0.0-  2.6  green 

tetraethyl-di-p-amino- 

triphenyl-carbinol 

74 

Iodine  green 

yellow 

0.0-  2.6  blue 

heptamethyl  rosaniline 

75 

Ethyl  violet  (518) 

yellow 

0.0-  3.6  blue 

hexaethyl  pararosaniline 

76 

Ethyl  green  (methyl  green)... 
ethyl-hexamethyl-para- 
rosaniline  bromid 

0.1-  2.3 

CHOICE    OF   INDICATORS                                              89 

TABLE  11- 

■Continued 

tERIAL 
NUM- 
BER 

77 

78 
79 
80 

81 
82 

INDICATOR 

pH  RANGE 

Methyl  violet  6B  extra  (517).. 
mixture  of  benzyl-tetra- 
and         pentamethyl-p- 
rosaniline     and     hexa- 
methyl-p-rosaniline 

Fuchsin  (512)  (base) 

0.1-  3.2 

purple    1.2-  3.0  fades 
pink    3.6-  6.0  colorless 

mixture  of  rosaniline  and 
pararosaniline 
Red  violet  5ES  (525) 

trisulfonate  of  ethyl  ro- 
saniline 
Water  blue  (539) 

blue    4.7-  7.0  colorless,* 

di-  and  tri-sulfonic  acids 

of    triphenyl-p-rosani- 

line  and  di-phenyl-ro- 

saniline 

Aurin  (p-rosolic  acid)  (555)... 

complex  mixture 
Alkali  blue  (536) 

purple  10.5- 
14.0  rose 

yellow    6.9-  8.0  red 
lilac    9.4-14.0  pink 

83 

mixture  of  diphenyl-ro- 
saniline-mono-sulfonic 
acid  and  triphenyl- 
pararosaniline-mono- 
sulfonic  acid 
Methyl  blue  (538) 

blue  10.0-13.0  pink 

84 

triphenylpararosaniline- 
di-  and  trisulf  onic  acids 
Fuchsin  S  (524) 

red  12.0-14.0  fades 

di-  and  trisulfonic  acids 
of  rosaniline  and  p-ro- 
saniline 

*  Samples  of  Water  blue  (China  blue)  which  we  have  tested  vary  con- 
si  lerably.  The  color  change  in  the  neutral  range  is  instantaneous  with 
s<  me  samples  but  requires  a  long  period  (several  hours  at  room  tempera- 
t\  re)  for  others. 

TABLE  12 
Quinoline  compounds 


81  RIAL 
1   OTH- 
ER 

INDICATOR 

pH  RANGE 

55 

Quinoline  blue  (Cyanin)  (611). 
C28H35N2I 

colorless    7.0-8.0   violet 

TABLE  18 
Oxazine  compounds 


SERIAL 

NUM- 

INDICATOR 

pH  RANGE 

BER 

86 

Alizarin  green  B  (657) 

lilac-0.3-  1.0  flesh, 

dihydroxy-naphth-azox- 

brownish  yel- 

onium sulfonate 

low  12.0- 
14.0  brown, 
then   green 

87 

Nile  blue  2B  (654) 

blue    7.2-  8.6  rose 

diethyl-benzyl-diamino- 

naphtho-phenazoxon- 

ium  chlorid 

88 

Nile  blue  A  (653) 

blue  10.2-13.0  rose 

diethyl-diamino-naphtho- 

phenazoxonium  sulfate 

TABLE  14 

Azines 


SERIAL 

NUM- 

INDICATOR 

pH  RANGE 

BER 

89 

Methylene  violet  BN  powder 

(680) 

purple 

0.0-  1.2  violet 

dimethyl-diamino- 

phenyl-phenaz  onium 

chloride 

90 

Rosolane  (688) 

0.1-  2.9 

phenyl  and  tolyl 

safranines 

91 

Rose  magdala  (694) 

rose 

3.0-  4.0  red, 

mixtures  of  amino  naph- 

lilac  12.0- 

thyl-naphthazonium 

14.0  violet 

chlorid  and  diamino- 

n  aphthy  1-n  aphthaz  on- 

ium chloride 

92 

Indulin,  spirit  soluble  (697) . . 
mixtures  of  dianilido- 
amido-tri-anilido-  and 
tetranilido-phenyl- 
phenazonium  chlorides 

blue 

5.6-  7.0  violet 

93 

Neutral  red  (670) 

red 

6.8-  8.0  yellow 

dimethyl-diamino-tolu- 

phenazine 

94 

Neutral  blue  (676) 

9.3-10.2 

dimethyl-amino-phenyl- 

phenonaphthazonium 

chloride 

90 


CHOICE   OF  INDICATORS 


91 


TABLE  15 
Anthraquinone  compounds 


iERIAL 

NUM- 

INDICATOR 

pH  RANGI 

BER 

95 

Alizarin  Blue  X  (803) 

dihydroxy-anthra- 
quinone-/S-quinoline 

pink 

0.0-1.6 

yellow, 
yellow  6.0- 
7.6  green 

96 

Purpurin  (783) 

yellow 

0.0-4.0 

orange, 

1,  2, 4-trihydroxy-anthra- 

orange  4.0- 

qumone 

8.0  rose, 
lilac  12.0- 
14.0  violet 

97 

Alizarin  red  S  (780) 

yellow 

5.0-6.8 

pink 

mono  sulfonic  acid  of 

alizarin  Vi 

98 

Alizarin  Vi  (Alizarine)  (778)... 
1,  2-dihydroxy-anthra- 
quinone 

yellow 

5.5-6.8 

red, 

violet  10.1- 
12.1  purple 

99 

Alizarin  Blue  S  (804) 

yellow 

6.0-8.0 

green, 

Na  bisulfite  compound  of 

green  11.0- 

alizarin  blue  X 

13.0  blue 

TABLE  16 
Indigos 


E  3RIAL 
DUM- 
BER 


.00 


INDICATOR 


Indigotine  la  in  powder  (In- 
digo carmine)  (877) . . . 
Indigo  disulfonate 


pH  RANGE 


blue  11.6-14.0  yellow 


92 


THE  DETERMINATION  OF  HYDROGEN  IONS 


TABLE  17 
Phthalein  and  xanthone  compounds 


SERIAL 

NUM- 
BER 

INDICATOR 

pH  RANGE 

101 

Rhodamine  B  (573) 

orange - 
yellow 

orange 

orange 

pink 

light  yellow 

yellow 

yellowish 
yellowish 
colorless 
colorless 
colorless 
colorless 
colorless 
pink 

-0.1-  1.2  pink 
0.0-  2.6  brown, 

102 

diethyl  m-amino-phenol- 
phthalein 
Gallein  (599) 

103 

pyrogallol  phthalein 
E©sin  G  (587) 

brown  3.6- 
7.0  pink, 

pink  9.4- 
14.0  purple 
0.0-  3.0  pink 

0.0-  3.6  pink 

1.4-  3.6  red 

3.6-  5.6  yellow  (fluo- 
rescent) 

4.0-  6.6  yellow  (fluo- 
rescent) 

7.0-  9.0  green 

7.0-  9.0  blue 

8.0-  9.0  violet 

8.2-  9.8  red 

104 

tetrabromo  fluorescein 
Erythrosin* 

105 
106 

107 

Phloxin  Red  BH  (Griibler). . . 
Uranin  (Fluorescein)  (585) . . . 

resorcin  phthalein 
Dichloro  fluorescein 

108 
109 
110 
111 

o-a-Naphthol  phthalein 

p-a-Naphthol  phthalein 

Tetrabromophenol  phthalein. 
o-Cresol  phthalein 

112 

Phenol  phthalein 

8.3-10.0  red 

113 

114 

1,  2,  3-Xylenol  phthalein 

Thymol  phthalein 

8.9-10.2  blue 
9.3-10.5  blue 

115 

Eosin  BN  (590) 

10.5-14.0  yellow 

dibromo  dinitro  fluo- 
rescein 

*  The  identity  of  this  erythrosin  is  in  doubt.  Erythrosin  R,  G,  yellow- 
ish, and  Iodeosin  G  are  synonyms  of  di-iodo-fluorescein.  Erythrosin  extra 
bluish,  D,  B,  J  extra,  JNV,  W  extra,  and  Iodeosin  B  are  synonyms  for  the 
tetra-iodo-fluorescein . 


CHOICE    OF   INDICATORS 


93 


TABLE  18 
Sulfonphthaleins 


SERIAL 

NUM- 

INDICATOR 

pH  RANGE 

BER 

116 

Di-iodophenol  sulfon- 

phthalein* 

orange 

0.0-  1.2  yellow, 

yellow  3.2- 

/ 

7.0  purple 

117 

pink 

0.2-  0.8  orange, 

yellow  4.0- 

7.0  green, 
violet  8.5- 

10.2  blue, 
blue  10.2- 

12.5  green 

118 

Thymol  sulf  onphthalein 
Thymol  blue 

(acid  range) 

red 

1.2-  2.8  yellowf, 

(alkaline  range) 

yellow  8.0- 

119 

Tetranitrophenol  sulfon- 

9.6  blue 

phthalein 

yellow 

2.8-  3.8  red 

120 

Tetrabromophenol  sulfon- 

phthalein 

yellow 

3.0-  4.6  blue 

Brom  phenol  blue 

121 

Tetrachlorophenol  sulf  on- 

phthalein  

•  yellow 

3.0-  4.6  blue 

122 

Dibromo-o-cresol  sulfon- 

phthalein 

yellow 

5.2-  6.8  purple 

Brom  cresol  purple 

.23 

Dibromothymol  sulfon- 

phthalein 

yellow 

6.0-  7.6  blue 

Brom  thymol  blue 

24 

Phenol  nitro  sulf  onphthalein. 

yellow 

6.6-  8.4  purple 

25 

Phenol  sulf  onphthalein 

Phenol  Red 

yellow 

6.8-  8.4  red 

26 

o-Cresol  sulfonphthalein 

Cresol  Red 

yellow 

7.2-  8.8  red 

27 

Salicyl  sulfonphthalein 

yellow 

7.2-  9.2  pink 

28 

Thymol  nitro  sulfonphthalein. 

yellow 

7.2-  9.4  blue 

29 

a-Naphthol  sulfonphthalein . . 

yellow 

7.5-  9.0  blue 

30 

Carvacrol  sulfonphthalein 

yellow 

7.8-  9.6  blue 

31 

Orcin  sulfonphthalein 

yellow 

8.6-10.0  pink    (fluo- 
rescent) 

32 

Nitrothymol  sulfonphthalein. 

violet 

9.2-11.5  yellow 

*  Purity  not  established. 

f  All  sulfonphthaleins  show  color  changes  at  high  acidities  but  those 
o  thymol  sulfonphthalein  are  the  most  useful. 


TABLE  19 
Miscellaneous  indicators 


SERIAL 

NUM- 

INDICATOR 

pH  RANGE 

BER 

133 

Croceine  (?) 

■   blue- 

-0.3-  0.0  rose, 

rose  12.0- 

14.0  violet 

134 

green 

-0.3-  1.0  blue, 

violet  14.0- 
15.0  lilac 

135 

Safranin  (679?) 

blue- 

-0.3-  1.0  red, 

red   14.0- 
15.0  violet 

136 

Hematein  (Logwood)  (938)  . . . 

variable 

from 

0.0-15.0 

137 

Gentian  violet 

0.4-  2.7 

138' 

Red  cabbage  extract 

red 

2.4-  4.5  green 

139 

1-Oxy-naphtho-chino- 

methane 

colorless 

2.7-  3.7  purple 

2.8-  4.0  yellow 

140 

Troger  and  Hille's  indicator. . 

orange 

C14H16N4SOsH 

< 

141 

Phenacetolin 

yellow 

3.0-  6.0  red, 

red   10.0- 

13.0  colorless 

142 

Lacmosol 

red 
red 
red 

4.4—  5.5  blue 

143 

Lacmoid 

4.4-  6.2  blue 

144 

Azolitmin  (Litmus) 

4.5-  8.3  blue 

145 

Carminic  acid   (from  cochi- 

neal) (932) '. 

orange 

4.6-  7.8  rose, 

violet  11.0- 

14.0  pink 

146 

Cochineal  (932) 

yellow 
pink 

4.8-  6.2  lilac 

147 

Archil  (Orchil)  (934) 

5.6-  7.6  lilac 

148 

Brazil  wood,  Redwood,  Bra- 

silein  (935) 

colorless 

6.0-  8.0  pink 
7.0-  8.0  greenish 
7.3-  8.7  green 

149 

Guaiac  tincture 

colorless 

150 

Lygosine 

yellow 

di-o-hydroxy-styryl 

ketone 

151 

Mimosa  flower  extract 

7.7-  9.6 

152 

Turmeric  (Curcuma)  (927)  . . . 
C21H20O6 

yellow 

8.0-10.2  orange 

153 

Alkanin 

red 
yellow 
purple 
orange 

8.3-10.0  blue 

154 

a-Naphthol  benzein 

8.5-  9.8  green 

155 

Benzoazurin  (?) 

10.5-12.0  pink 
11.0-12.0  orange  red 

156 

Helianthin  I  (?) 

157 

Poirrier's  blue 

blue 
brownish- 
yellow 

11.0-13  0  red 

158 

Helianthin  II  (?) 

13.0-14.0  lilac 

94 


CHOICE    OF   INDICATORS 


95 


TABLE  20 
The  more  common  synonyms  of  indicators 

This  table  contains  the  names  and  synonyms  of  the  various  indicators 
in  alphabetical  order.  Following  each  name,  or  group  of  synonyms,  is  a 
number  in  bold  face  type.  This  number  is  the  serial  number  of  the  com- 
pound as  found  in  the  preceding  tables. 

Some  names  apply  to  two  or  more  entirely  different  dyes.  If  such  dyes 
are  in  our  tables,  their  serial  numbers  are  given;  and  if  the  particular  dyes 
are  not  in  the  preceding  tables  there  is  given  in  italics  in  parentheses  the 
1914  Schultz  number  and  name.  Thus:  "Helianthin,  36,  41  (141,  Azogelb 
SG  cone.),"  means  that  the  name  Helianthin  is  applied  to  Orange  III,  to 
Methyl  orange  and  to  Schultz  No.  141,  Azogelb  3G  cone. 


Acetin  blue  R 92 

Acid  fuchsin,  B,  G,  O,  S 84 

Acid  magenta,  0 84 

Acid  orange 60 

Acid  yellow,  cryst,  D  extra,  DMP 25 

Acid  yellow  RS 65 

Acme  yellow 65 

Alizarin,  le 98 

Alizarin-Blaustich  I  and  la 98 

Alizarin  blue  A,  ABI,  BM  in  Teig,  C, 
DNW  in  Teig,  F,  G,  GG,  GW,  R, 
RR,  RR  in  Teig,  WA  in  Teig,  WC, 
WN  in  Teig,  WR,  WRR,  WX,  X,  XA 

in  Teig 95 

Alizarin  blue  S,  SR,  SRW,  SW 99 

Alizarin  blue  soluble  ABS 99 

Alizarin  carmine 97 

Alizarin  dark  blue  S,  SW 99 

Alizarin  green  B 86 

Alizarin  mono  sulfonate 97 

Alizarin  No.  1 98 

Uizarin  No.  6 96 

Uizarin  orange  R,  2R-paste  and  powder..  62 

Uizarin  P 98 

Uizarin  powder  SA,  W,  W  extra 97 

dizarin  purpurin 96 

dizarin  red  IWS,  S 97 

.  dizarin  sulfacid 97 

.  dizarin  yellow  G,  GG,  GGW,  3G  paste 

and  powder 61 

.  dizarin  yellow  R,  RW  paste  and  powder  62 

.  lizarin  VI 98 

.  lizarin  violet 102 

L  lkah"  blue,  B-5B,  No.  2,  No.  4,  No.  6, 

R-5R,  RR 82 

i  lkanin , 153 

i  midoazobenzol 30 

i  nilin  brown 78 

i  nilin  purple 90 

i  nilin  red 78 

i  nilin  yellow 3,  30 

i  nthracene  yellow  GG 61 


Anthracene  yellow  RN 62 

Anthracene  violet 102 

Anthraquinone  compounds Table  15 

Archelline  2B ." . . .  64 

Archil 147 

Atlas  orange 60 

Aurin 81 

Azalein 78 

Azin  blue  spirit  soluble 92 

Azines Table  14 

Azo  blue 69 

Azo-bordeaux 64 

Azolitmin 144 

Azo  compounds Table  9 

Baumwollrot  4B 68 

(.363,  Benzopurpurin  4B) 

Baumwollrot  B 67,    68 

Baumwollrot  C 68 

Beizengelb2  GT 61 

Beizengelb  3R,  PN 62 

Benzal  green  00 71 

Benzoazurin 155 

Benzoin  blue  R 69 

Benzopurpurin  B 67 

Benzyl  violet,  7B 77 

Betanaphthol  orange 60 

Bitter  almond  oil  green 71 

Blau  CB,  spirit  sol 92 

Bleu  alcalin,  4B 82 

Bleu  3BS,  C4B,  de  Lyon  0 80 

Bleu  methyl 83 

Bleu  neutre 94 

Bleu  Nicholson  4B ' 82 

Bleu  soluble  pur 80 

Blue  extra,  water  soluble  for  wool  and 

silk 80 

Bogert  and  Scatchard's  indicator 11 

Bordeaux  B,  BL,  R,  R  extra 64 

Bordeaux  G 64 

(254,  Bordeaux  G) 

Brasilein;  brasilin 148 

Braun  salz  R 47 


96 


THE  DETERMINATION  OF  HYDROGEN  IONS 


TABLE  20- Continued 


Brazil  wood 148 

Brilliant  f  uchsin 78 

Brilliant  green,  crystals,  cryst.  No.  1,  3, 

4,  extra,  II,  O,  S,  Y 73 

Brilliant  violet  6B,  8B 77 

Brom  cresol  purple 122 

Brom  eosin 103 

Brom  phenol  blue 120 

Brom  thymol  blue 123 

Butter  yellow  0 37 

Campeche  wood 136 

Cardinal,  R,  G 78 

Cardinal  red 63 

Cardinal  red  B,  G,  R 78 

Carmine,  lake 146 

Carminic  acid 145 

Cerasin 63 

Cerasine,  R ' 64 

China  blue 80 

China  green  cryst 71 

Chrombrown  RO 57 

Chrysoidin 47 

(84,  Chrysoidin  R) 
Chrysoidin  A  cryst.,  -Fettfarbe,  G,  2G 

extra,  J,  JEE,  RE,  Y,  Y  extra 47 

Chrysoidin  R 47 

(34  also  69,  Chrysoidin  R) 

Chrysoin,  G 65 

Citronine  V  double 25 

Cochineal 146 

Congo;  Congo  red;  Congo  red  R 68 

Corallin 81 

Cotton  blue 80,    83 

Cotton  blue  3B,  cone.  No.  1,  No.  2,  cone. 

R,  extra 80 

Cotton  red  B 67,    68 

Cotton  red,  cone 68 

Cresol  red 126 

Croceine 133 

Crystal  violet,  extra  cryst.  5B,  5BO,  6B, 

N  powder,  O,  P  cryst 70 

Cudbear 147 

Curcuma 152 

Curcumein* 16 

Curcumin 152 

Cyanin 85 

Dahlia 72 

Dechan's  indicator 102 

Degener's  indicator 141 

Diamant  f  uchsin 78 

Diamant  griin 71 

Diamant  grttn  B 71 

(276,  Diamantgrun  B) 

Diamant  grttn  G 73 

Dianilrot  R 68 

Disazo  compounds Table  10 

Dianthine  B 104 


Dichlorofluorescein 107 

Dimethylaniline  orange 41 

Diphenylamin  blue 83 

Direct  red  C 68 

Ecarlate  J,  JJ,  V 115 

Echtblau  B  spirit  sol.,  R  spirit  sol 92 

EchtbraunN 57 

Echtgrttn 71 

(1,  SolidgrUn  O  in  Teig) 

Echtrot  A,  AV,  0 63 

Echtrot  B,  P  extra 64 

Emerald  green  cryst 71 

Eosine  bleuatre,  bluish 104 

Eosin,  B  extra,  DH,  extra  water  sol.,  G, 
G  extra,  GGF,  2G,  I  yellowish,  J 
extra,  JJF,  3J,  4J  extra,  KS  ord.,  MP, 
OO  extra,  S  extra  yellowish,  yellowish, 

Y  extra 103 

Eosin  B,  BN,  BW,  DHV,  I  blfiulich,  S 

extra  bluish 115 

Eosin  J 104 

Eosin  methylene  blue 134 

Eosin  scarlet,  B,  BB  extra 115 

Erythrosin  B,  bluish,  extra  bluish,   D, 

J  extra,  JNV,  W  extra 104 

Ethyl  green 73,    76 

Ethyl  orange 42 

Ethyl  red 51 

Ethyl  purple  6B 75 

Ethyl  violet 75 

Fast  brown  N 57 

Fast  pink  for  silk 91 

Fast  red  A 63 

Fast  red  B,  P  extra 64 

Fast  red  cone 63 

Fluorescein 106 

Formanck's  indicator 86 

Fuchsia 89 

Fuchsin  acid 84 

Fuchsin  base 78 

Fuchsin,  6B,  crystals,  FCOO,  la  cryst., 

NB,  NG,  RFN,  VI  cryst.,  XL 78 

Fuchsin  S,  SIII,  SN,  SS,  ST 84 

Fustic 72,    84 

Galleln,  paste  A,  SW,  W  paste  and  powder  102 

Gentian  violet 137 

Gold  orange 60 

Gold  orange  MP 41 

Gold  yellow 3,    65 

Green  crystals 71 

Guernsey  blue 80 

Guaiac  tincture 149 

Hematein;  Hematoxylin 136 

Helianthin 36,    41 

(141,  Azogelb  SG  cone.) 

Helianthin  1 156 

Helianthin  II 158 


*  The  term  curcumein  has  been  applied  to  several  different  compounds. 


CHOICE   OF  INDICATORS 


97 


TABLE  20— Continued 


Helvetia  blue 83 

Henderson  and  Forbes'  indicator 5 

Hof  mann's  violet 72 

Indigen  D,  F 92 

Indigo  carmine,  carmine  D  paste,  disul- 

fonate,  extract 100 

Indigos Table  16 

Indigotine  la  powder 100 

Indophenin  extra 92 

Indulin  base,  2B,  BA,  opal,  spirit  soluble, 

RA 92 

Iodeosin  B 104 

Iodine  green 74 

Jaune  beurre 37 

Jaune  chrome  R 61 

Jaune  d'aniline 30 

Jaune  d'or 3 

Jaune  II 65 

Jaune  M,  mfitanile  extra  230 23 

Jaune  naphtol 3 

(7,  Naphtolgelb  S) 

Iodeosin  B 104 

Todviolett 72 

Kaiserrot 115 

Kosmosrot  extra 68 

Kristallorange  GG 66 

jacmosol 142 

'-.acmoid 143 

jacmus 144 

.lichtblau  G 80 

.light  green  N 71 

.litmus 144 

.ogwood 136 

juck's  indicator 113 

iUnge's  indicator 41 

:  ,yddit 1 

.  ivgosine 150 

]  fagdala  red 91 

1  [agenta 78 

]  [alachite  green,  A  cryst.,  B,  cryst.  extra, 
cryst.  3,  cryst.  4,  powder  superfine  B, 

4B 71 

I  Calachite  green  G 73 

1  "anchester  yellow. 3 

1  landarin  G 60 

1  !arine  blue  V 80 

I  artius  yellow 3 

I  auvein 90 

J  elinite 1 

J  ellet's  indicator 58 

J  etachrome  orange  R 62 

J  etanil  yellow,  extra,   GR  extra  cone, 

O,  PL 23 

I  ethyl  blue,  for  cotton,  MBJ,  MLB 83 

J  ethylene    violet    BN    powder,    RRA, 

RRN,  3RA  extra 89 

J  ethyl  eosin  B  extra 115 


Methyl  green 76 

Methyl  orange,  MP 41 

Methyl  red 50 

Methyl  violet  5B,  6B,  6B  extra,  7B,  10B. .  77 

Methyl  water  blue 83 

Mimosa  extract , 151 

Miscellaneous  indicators Table  19 

Naphthalene  red,  rose 91 

Naphthalene  yellow 3 

a-naphthol  benzein 154 

a-naphthol  orange 59 

Naphthol  orange 59 

Naphthol  yellow 3 

(7,  Naphtolgelb  S) 

Naphthylamin  brown 57 

Naphthylamin  pink 91 

Naphthylamin  yellow 3 

Natural  indicators Table  19 

Neutral  blue 94 

Neutral  red,  extra 93 

New  green,  cryst.,  BI,  BII,  Bill,   GI, 

Gil,  GUI 71 

New  Victoria  green  I,  II,  0 71 

New  yellow  extra 25 

Nicholson's  blue 82 

Nierenstein's  indicator 139 

Nile  blue  A,  B,  R 88 

Nile  blue  2B 87 

Nitramine  (?) 13 

Nitro  compounds,  Nitro-phenols Table  8 

NopalinG 115 

Oil  yellow 37 

(36,  Sudan  I) 

Opal  blue  bluish 80 

Orange  A 60 

Orange  B 59 

Orange  extra 60 

Orange  G 60,    66 

(36,  Sudan  I) 

Orange  GG,  GG  in  cryst.,  GMP 66 

Orange  GS,  IV 25 

Orange  1 59 

Orange  II,  IIB,  IIP,  IIPL 60 

Orange  III 36,    41 

Orange  MN,  MNO 23 

Orange  N 25 

(79,  Brillantorange  R) 

Orange  No.  1 59 

Orange  No.  2 60 

Orange  No.  3 36,    41 

Orange  No.  4 25 

Orange  P 60 

Orange   R 62 

(39,  Ponceau  G;  151,  Orange  T) 

Orange  R  extra 59,  60 

Orange  S 59 

Orangd  au  chrome 62 


98 


THE  DETERMINATION  OP  HYDROGEN  IONS 


TABLE  20— Concluded 


Orcein;  Orchil 147 

Orcellin  No.  4 63 

Orseille,  carmine,  extract 147 

Oxazine  compounds Table  13 

Para  methyl  red 20 

Paris  violet  6B,  7B 77 

Patent  orange 66 

Perkin's  violet 90 

Phenacetolin 141 

Phenol  red 125 

Phenolphthaleins Table  17 

Phenolsulfonphthaleins Table  18 

Phloxin  red  BH 105 

Phthaleins Table  17 

i-picramic  acid 8 

Picric  acid 1 

Poirrier's  blue 157 

Poirrier's  orange  II 60 

Pourpre  francaise 147 

Primerose  soluble 104 

Primula  R  water  sol 72 

Propyl  red 52 

Purpurin ' 96 

Pyrosin  B '. 104 

Quinoline  blue 85 

Quinoline  compounds Table  12 

Red  cabbage 138 

Red  violet,  5R  extra 72 

Red  violet  5RS 79 

Redwood 148 

Resorcin  yellow 65 

Rhodamine  B,  B  extra,  0 101 

Roccellin 63 

Rosanilin  base 78 

Rose  B  a  l'eau 104 

Rosein 78 

Rose  magdala 91 

Rosolane 90 

Rosolic  acid 81 

Rouge  B 64 

Rouge  1 63 

Rouge  congo '. 68 

Rouge  coton  G,  direct  C 68 

Rouge  neutre  extra 93 

Rubidin 63 

Rubin 78 

Safranin 135 

Safranin  extra  bluish 89 

Safrosin 115 


Saure  gelb  cryst.,  D  extra,  DMP 25 

Saure  orange. 60 

Silk  blue,  BTSL 80 

Smaragdgrun  cryst 73 

Solid  blue  base,  B  spirit  sol.,  RR 92 

Solid  green  J,  JJO 73 

Solid  green  4B,  cryst.  A  No.  1,  cryst.  O, 

cryst.  OO,  extra  J,  O,  OOJ,  P 71 

Soluble  blue 80 

(687,  Methylblau  fur  Seide  MLB) 

Spirit  induline,  B,  R  cone 92 

Spirit  yellow,  G 30 

Sudan  red 91 

Sulfonphthaleins Table  18 

Terra  cotta  R 62 

Tymol  blue 118 

Tournesol 144 

Triphenylme  thane  dyes Table  1 1 

Troger  and  Hille's  indicator 140 

Tropaeolin  G 23,    59 

Tropaeolin  O 65 

Tropaeolin  OO 25 

Tropaeolin  OOO  No.  1 59 

Tropaeolin  OOO  No.  2 60 

Tropaeolin  R 65 

Turmeric 152 

Uranin 106 

Vert  brillant 73' 

Vert  diamond  P  extra 71 

Vert  ethyle  extra 73 

Vert  J3E,  solide  B  extra,  LB  extra,  solide 

cristaux  0 71 

Victoria  yellow  O  double  cone 23 

Violet  5B,  6B,  7B 77 

Violet  7B  extra 70 

Violet  au  bichromate 90 

Violet  benzyle 77 

Violet  C,  G 70 

Violet  Hofmann 72 

Violet  meHhyl  6B,  6B  extra  cone 77 

Violet  pate 90 

Violett  R,  RR,  4RN 72 

Von  M  tiller's  indicator 25 

Walkorange  R 62 

Water  blue,  B,  BJJ,  R 80 

Wool  blue 83 

Xanthone  compounds Table  17 

Yellow  corallin 81 


CHAPTER  VI 
Standard  Buffer  Solutions  for  Colorimetric  Comparison 

The  standard  solutions  used  in  the  colorimetric  method  of 
determining  hydrogen  ion  concentrations  are  buffer  solutions  with 
such  well  defined  compositions  that  they  can  be  accurately  repro- 
duced, and  with  pH  values  accurately  defined  by  hydrogen  elec- 
trode measurements.  They  generally  consist  of  mixtures  of  some 
acid  and  its  alkali  salt.  Several  such  mixtures  have  been  care- 
fully studied.  An  excellent  set  has  been  described  by  S.^rensen 
(1912).  This  set  may  be  supplemented  by  the  acetic  acid — 
sodium  acetate  mixtures,  most  careful  measurements  of  which 
have  been  made  by  Walpole  (1914),  and  by  Palitzsch's  (1915) 
excellent  boric  acid-borax  mixtures. 

Clark  and  Lubs  (1916)  have  designed  a  set  of  standards  which 
they  believe  are  somewhat  more  conveniently  prepared  than 
are  the  S0rensen  standards.  Their  set  is  composed  of  the  follow- 
ing mixtures: 

Potassium  chlorid  +  HC1 
Acid  potassium  phthalate  +  HC1 
Acid  potassium  phthalate  +  NaOH 
Acid  potassium  phosphate  +  NaOH 
Boric  acid,  KC1  +  NaOH 

For  a  discussion  of  these  mixtures,  the  methods  used  in  deter- 
mining their  pH  values,  and  the  potential  measurements  we  refer 
ihe  reader  to  the  original  paper  {Journal  of  Biological  Chemistry, 
1916,  25,  no.  3,  p.  479).  We  may  proceed  at  once  to  describe  the 
letails  of  preparation. 

The  various  mixtures  are  made  up  from  the  following  stock  solu- 
tions: M/5  potassium  chlorid  (KC1),  M/5  acid  potassium  phos- 
)hate  (KH2P04),  M/5  acid  potassium  phthalate  (KHC8H404), 
Vl/5  boric  acid  with  M/5  potassium  chlorid  (H3BO3,  KC1),  M/5 
odium  hydroxid  (NaOH),  and  M/5  hydrochloric  acid  (HC1). 
Uthough  the  subsequent  mixtures  are  diluted  to  M/20  the  above 
oncentrations  of  the  stock  solutions  are  convenient  for  several 
easons. 

99 


100  THE   DETERMINATION   OF   HYDROGEN   IONS 

The  water  used  in  the  crystallization  of  the  salts  and  in  the 
preparation  of  the  stock  solutions  and  mixtures  should  be  redis- 
tilled. So-called  "conductivity  water,"  which  is  distilled  first 
from  acid  chromate  solution  and  again  from  barium  hydroxid,  is 
recommended,  but  it  is  not  necessary. 

M/5  potassium  chlorid  solution.  (This  solution  will  not  be 
necessary  except  in  the  preparation  of  the  most  acid  series  of 
mixtures.)  The  salt  should  be  recrystallized  three  or  four  times 
and  dried  in  an  oven  at  about  120°C.  for  two  days.  The  fifth 
molecular  solution  contains  14.912  grams  in  1  liter. 

M/5  acid  potassium  phthalate  solution.  Acid  potassium  phtha- 
late  may  be  prepared  by  the  method  of  Dodge  (1915)  modified 
as  follows.  Make  up  a  concentrated  potassium  hydroxid  solu- 
tion by  dissolving  about  60  grams  of  a  high-grade  sample  in 
about  400  cc.  of  water.  To  this  add  50  grams  of  the  commer- 
cial resublimed  anhydrid  of  ortho  phthalic  acid.  Test  a  cool  por- 
tion of  the  solution  with  phenol  phthalein.  If  the  solution  is  still 
alkaline,  add  more  phthalic  anhydrid;  if  acid,  add  more  KOH. 
When  roughly  adjusted  to  a  slight  pink  with  phenol  phthalein1 
add  as  much  more  phthalic  anhydrid  as  the  solution  contains  and 
heat  till  all  is  dissolved.  Filter  while  hot,  and  allow  the  crystal- 
lization to  take  place  slowly.  The  crystals  should  be  drained 
with  suction  and  recrystallized  at  least  twice  from  distilled  water.2 

Crystallization  should  not  be  allowed  to  take  place  below 
20°C,  for  Dodge   (1920)   states: 

A  saturated  solution  of  the  acid  phthalate  on  chilling  will  deposit 
crystals  of  a  more  acid  salt,  having  the  formula  2KHC8H404-C8Hg04. 
These  crystals  are  in  the  form  of  prismatic  needles,  easily  distinguished 
under  the  microscope  from  the  6-sided  orthorhombic  plates  of  the  salt 
KHCH4O4. 

Dry  the  salt  at  110°-115°C.  to  constant  weight. 

A  fifth  molecular  solution  contains  40.836  grams  of  the  salt  in 
1  liter  of  the  solution. 

M/5  acid  potassium  phosphate  solution.  A  high-grade  com- 
mercial sample  of  the  salt  is  recrystallized  at  least  three  times 

1  Use  a  diluted  portion  for  the  final  test. 

2  Samples  of  phthalic  anhydrid  which  are  now  found  on  the  market  are 
frequently  grossly  impure.  With  some  samples  ten  recrystallizations 
are  necessary.    Hence  it  is  economy  to  purchase  only  the  highest  grades. 


STANDARD    BUFFER   SOLUTIONS  101 

from  distilled  water  and  dried  to  constant  weight  at  110°-115°C. 
A  fifth  molecular  solution  should  contain  in  1  liter  27.232  grams. 
The  solution  should  be  distinctly  red  with  methyl  red  and  dis- 
tinctly blue  with  brom  phenol  blue. 

M/5  boric  acid,  M/5  potassium  chlorid.  Boric  acid  should  be 
recrystallized  several  times  from  distilled  water.  It  should  be 
air  dried3  in  thin  layers  betweeri  filter  paper  and  the  constancy 
of  weight  established  by  drying  small  samples  in  thin  layers  in  a 
desiccator  over  CaCl2.  Purification  of  KC1  has  already  been 
noted.  It  is  added  to  the  boric  acid  solution  to  bring  the  salt 
concentration  in  the  borate  mixtures  to  a  point  comparable  with 
that  of  the  phosphate  mixtures  so  that  colorimetric  checks  may 
be  obtained  with  the  two  series  where  they  overlap.  One  liter 
of  the  solution  should  contain  12.40484  grams  of  boric  acid  and 
14.912  grams  of  potassium  chlorid. 

M/5  sodium  hydroxid  solution.  This  solution  is  the  most  diffi- 
cult to  prepare,  since  it  should  be  as  free  as  possible  from  carbon- 
ate. A  solution  of  sufficient  purity  for  the  present  purposes  may 
be  prepared  from  a  high  grade  sample  of  the  hydroxid  in  the 
following  manner.  Dissolve  100  grams  NaOH  in  100  cc.  distilled 
water  in  a  Jena  or  Pyrex  glass  Erlenmeyer  flask.  Cover  the 
mouth  of  the  flask  with  tin  foil  and  allow  the  solution  to  stand 
over  night  till  the  carbonate  has  settled.  Then  prepare  a  filter 
as  follows.  Cut  a  "hardened  "  filter  paper  to  fit  a  Buchner  funnel. 
Treat  it  with  warm,  strong  [1:1]  NaOH  solution.  After  a  few 
minutes  decant  the  sodium  hydroxid  and  wash  the  paper  first 
with  absolute  alcohol,  then  with  dilute  alcohol,  and  finally  with 
large  quantities  of  distilled  water.  Place  the  paper  on  the  Buch- 
ner funnel  and  apply  gentle  suction  until  the  greater  part  of  the 
water  has  evaporated;  but  do  not  dry  so  that  the  paper  curls. 
Now  pour  the  concentrated  alkali  upon  the  middle  of  the  paper, 
spread  it  with  a  glass  rod  making  sure  that  the  paper,  under 
gentle  suction,  adheres  well  to  the  funnel,  and  draw  the  solution 

*  Boric  acid  begins  to  lose  "water  of  constitution"  above  50°C. 

*  This  weight  was  used  on  the  assumption  that  the  atomic  weight  of 
boron  is  11.0.  The  atomic  weight  has  since  been  revised  and  appears  as 
10.9  in  the  1920  table. 

Because  the  solutions  were  standardized  with  the  above  weight  of  boric 
icid  this  weight  should  be  used. 


102  THE   DETERMINATION   OF   HYDROGEN   IONS 

through  with  suction.  The  clear  filtrate  is  now  diluted  quickly, 
after  rough  calculation,  to  a  solution  somewhat  more  concentrated 
than  N/1.  Withdraw  10  cc.  of  this  dilution  and  standardize 
roughly  with  an  acid  solution  of  known  strength,  or  with  a  sample 
of  acid  potassium  phthalate.  From  this  approximate  standardi- 
zation calculate  the  dilution  required  to  furnish  an  M/5  solution. 
Make  the  required  dilution  with  the  least  possible  exposure,  and 
pour  the  solution  into  a  paraffined5  bottle  to  which. a  calibrated  50 
cc.  burette  and  soda-lime  guard  tubes  have  been  attached.  The 
solution  should  now  be  most  carefully  standardized.  One  of  the 
simplest  methods  of  doing  this,  and  one  which  should  always  be 
used  in  this  instance,  is  the  method  of  Dodge  (1915)  in  which  use 
is  made  of  the  acid  potassium  phthalate  purified  as  already 
described.  Weigh  out  accurately  on  a  chemical  balance  with 
standardized  weights  several  portions  of  the  salt  of  about  1.6  grams 
each.  Dissolve  in  about  20  cc.  distilled  water  and  add  4  drops 
phenol  phthalein.  Pass  a  stream  of  C02-free  air  through  the 
solution  and  titrate  with  the  alkali  till  a  faint  but  distinct  and 
permanent  pink  is  developed.  It  is  preferable  to  use  a  factor 
with  the  solution  rather  than  attempt  adjustment  to  an  exact 
M/5  solution. 

If  one  should  be  fortunate  enough  to  find  that  the  concentrated 
sodium  hydroxid  solution  had  clarified  itself  without  leaving 
suspended  carbonate,  the  clear  solution  might  be  carefully  pi- 
petted from  the  sediment.  Cornog  (1921)  describes  another 
method  as  follows: 

Distilled  water  contained  in  an  Erlenmeyer  flask  is  boiled  to  remove 
any  carbon  dioxide  present,  after  which,  when  the  water  is  cooled  enough, 
ethyl  ether  is  added  to  form  a  layer  3  or  4  cm.  in  depth.  Pieces  of  metallic 
sodium,  not  exceeding  about  1  cm.  in  diameter  are  then  dropped  into  the 
flask.  They  will  fall  no  further  than  the  ether. layer  where  they  remain 
suspended.  The  water  contained  in  the  ether  layer  causes  the  slow  forma- 
tion of  sodium  hydroxid,  which  readily  passes  below  to  the  water  layer. 

8  The  author  finds  that  thick  coats  of  paraffine  are  more  satisfactory  than 
the  thin  coats  sometimes  recommended.  Thoroughly  clean  and  dry  the 
bottle,  warm  it  and  then  pour  in  the  melted  paraffine.  Roll  gently  to  make 
an  even  coat  and  just  before  solidification  occurs  stand  the  bottle  upright 
to  allow  excess  paraffine  to  drain  to  the  bottom  and  there  form  a  very  sub- 
stantial layer. 


STANDARD    BUFFER   SOLUTIONS  103 

Cornog  depends  upon  the  evaporation  of  the  ether  as  a  barrier 
to  CO2.  There  are  various  ways  in  which  the  protection  can  be 
made  more  sure,  and  there  are  also  various  ways  in  which  the 
aqueous  solution  may  be  separated  from  the  ether. 

From  time  to  time  there  appear  in  the  literature  suggestions 
regarding  the  use  of  barium  salts  to  remove  the  carbonate  in 
alkali  solutions. 

In  the  author's  opinion  the  next  step  to  take,  if  the  separation 
of  carbonate  from  very  concentrated  NaOH  solutions  is  not  con- 
sidered refined  enough  for  the  purpose  at  hand,  is  to  proceed 
directly  to  the  electrolytic  preparation  of  an  amalgam.  Given 
a  battery  and  two  platinum  electrodes  this  is  a  simple  process. 
A  deep  layer  of  redistilled  mercury  is  placed  in  a  conical  separa- 
tory  funnel.  The  negative  pole  of  the  battery  is  led  to  this 
mercury  by  a  glass-protected  platinum  wire.  Over  the  mercury 
is  placed  a  concentrated  solution  of  recrystallized  sodium 
chlorid  and  in  this  solution  is  dipped  a  platinum  electrode  con- 
nected with  the  positive  pole  of  the  battery.  The  battery  may 
be  4  to  6  volts.  Electrolysis  is  continued  with  occasional  gentle 
shaking  to  break  up  amalgam  crystals  forming  on  the  mercury 
surface. 

Boil  the  CO2  out  of  a  litre  or  so  of  redistilled  water,  and,  while 
steam  is  still  escaping,  stopper  the  flask  with  a  cork  carrying  a 
siphon,  a  soda-lime  guard  tube  and  a  corked  opening  for  the 
separatory  funnel. 

When  the  water  is  cool  introduce  the  delivery  tube  of  the  separa- 
tory funnel  and  deliver  the  amalgam.  Allow  reaction  to  take 
place  till  a  portion  of  the  solution,  when  siphoned  off  to  a 
burette  and  standardized,  shows  that  enough  hydroxid  has  been 
formed.  Then  siphon  approximately  the  required  amount  into  a 
boiled-out  and  protected  portion  of  water.  Mix  thoroughly  and 
standardize. 

M/5  hydrochloric  acid  solution.  Dilute  a  high  grade  hydro- 
chloric acid  solution  to  about  20  per  cent  and  distill.  Dilute  the 
distillate  to  approximately  M/5  and  standardize  with  the  sodium 
hydroxid  solution  previously  described.  If  convenient,  it  is  well 
to  standardize  this  solution  carefully  by  the  silver  chlorid  method 
and  check  with  the  standardized  alkali. 


104 


THE   DETERMINATION   OF   HYDROGEN   IONS 


10 


pH 


|T^ 

C^ 

\ 

\. 

D^- 

\ 

v  «r 

p 

2 

5 

50 

Fig.  11.  Clark  and  Lubs'  Standard  Mixtures 

A.  50  cc.  0.2m  KHPhthalate  +  X  cc.  0.2m  HC1.    Diluted  to  200  cc. 

B.  50  cc.  0.2m  KHPhthalate  +  X  cc.  0.2m  NaOH.    Diluted  to  200  cc. 

C.  50  cc.  0.2m  KH2PO<  +  X  cc.  0.2m  NaOH.    Diluted  to  200  cc. 

D.  50  cc.  0.2m  HsB03,  0.2m  KC1  +  X  cc.  0.2m  NaOH.    Diluted  to  200  cc. 


STANDARD    BUFFER    SOLUTIONS  105 

The  only  solution  which  it  is  absolutely  necessary  to  protect 
from  the  CO2  of  the  atmosphere  is  the  sodium  hydroxid  solution. 
Therefore  all  but  this  solution  may  be  stored  in  ordinary  bottles 
of  resistant  glass.  The  salt  solutions,  if  adjusted  to  exactly  M/5, 
may  be  measured  from  clean  calibrated  pipettes. 

These  constitute  the  stock  solutions  from  which  the  mixtures 
are  prepared.  The  general  relationships  of  these  mixtures  to 
their  pH  values  are  shown  in  figure  11.  In  this  figure  pH  values 
are  plotted  as  ordinates  against  X  cc.  of  acid  or  alkali  as  abscissas. 
It  will  be  found  advantageous  to  plot  this  figure  from  table  21  with 
greatly  enlarged  scale  so  that  it  may  be  used  as  is  S0rensen's 
chart  (1909).  The  compositions  of  the  mixtures  at  even  intervals 
of  0.2  pH  are  given  in  table  21. 

In  any  measurement  the  apportionment  of  scale  divisions 
should  accord  with  the  precision.  Scale  divisions  should  not  be 
so  coarse  that  interpolations  tax  the  judgment  nor  so  fine  as  to 
be  ridiculous.  What  scale  divisions  are  best  in  the  method  under 
discussion  it  is  difficult  to  decide,  since  the  precision  which  may 
be  attained  depends  somewhat  upon  the  ability  of  the  individual 
eye,  and  upon  the  material  examined,  as  well  as  upon  the  means 
and  the  judgment  used  in  overcoming  certain  difficulties  which 
we  shall  mention  later.  S0rensen  (1909)  has  arranged  the  stand- 
ard solutions  to  differ  by  even  parts  of  the  components,  a  system 
which  furnishes  uneven  increments  in  pH.  Michaelis,  (1910) 
on  the  other  hand,  makes  his  standards  vary  by  about  0.3  pH 
so  that  the  corresponding  hydrogen  ion  concentrations  are  approxi- 
mately doubled  at  each  step.  Certain  general  considerations 
lead  to  the  conclusion  that  for  most  work  estimation  of  pH  values 
to  the  nearest  0.1  division  is  sufficiently  precise,  and  that  this 
precision  can  be  obtained  when  the  nature  of  the  medium  per- 
mits if  the  comparison  standards  differ  by  increments  of  0.2  pH. 

It  is  convenient  to  prepare  200  cc.  of  each  of  the  mixtures  and 
to  preserve  them  in  bottles  each  of  which  has  its  own  10  cc. 
pipette  thrust  through  the  stopper. ,  It  takes  but  little  more  time 
to  prepare  200  cc.  than  it  does  to  prepare  a  10  cc.  portion,  and 
if  the  larger  volume  is  prepared  there  will  not  only  be  a  sufficient 
quantity  for  a  day's  work  but  there  will  be  some  on  hand  for  the 
occasional  test. 

Unless  electrometric  measurements  can  be  used  as  control,  we 


106 


THE  DETERMINATION  OP  HYDROGEN  IONS 


urge  the  most  scrupulous  care  in  the  preparation  and  preserva- 
tion of  the  standards.  We  have  specified  several  recrystallizations 
of  the  salts  used  because  no  commercial  samples  which  we  have 
yet  encountered  are  reliable. 


TABLE  21 

Composition  of  mixtures  giving  pH  values  at 
KC1-HC1  mixtures* 


\C.  at  intervals  of  0.2 


pH 

1.2 

50  cc. 

M/5  KC1 

64.5  cc. 

M/5  HC1 

Dilute  to  200  cc. 

1.4 

50  cc. 

M/5  KC1 

41.5  cc. 

M/5  HC1 

Dilute  to  200  cc. 

1.6 

50  cc. 

M/5  KC1 

26.3  cc. 

M/5  HC1 

Dilute  to  200  cc. 

1.8 

50  cc. 

M/5  KC1 

16.6  cc. 

M/5  HC1 

Dilute  to  200  cc. 

2.0 

50  cc. 

M/5  KC1 

10.6  cc. 

M/5  HC1 

Dilute  to  200  cc. 

2.2 

50  cc. 

M/5  KC1 

6.7  cc. 

M/5  HC1 

Dilute  to  200  cc. 

*  The  pH  values  of  these  mixtures  are  given  by  Clark  and  Lubs  (1916) 
as  preliminary  measurements. 

Phthalate-HCl  mixtures 

2.2      50  cc.  M/5  KHPhthalate      46 .70  cc.  M/5  HC1  Dilute  to  200  cc. 

2.4      50  cc.  M/5  KHPhthalate      39.60  cc.  M/5  HC1  Dilute  to  200  cc. 

2.6      50  cc.  M/5  KHPhthalate      32.95  cc.  M/5  HC1  Dilute  to  200  cc. 

2.8      50  cc.  M/5  KHPhthalate      26.42  cc.  M/5  HC1  Dilute  to  200  cc. 

3.0  '   50  cc.  M/5  KHPhthalate      20.32  cc.  M/5  HC1  Dilute  to  200  cc. 

3.2      50  cc.  M/5  KHPhthalate      14.70  cc.  M/5  HC1  Dilute  to  200  cc. 

3.4      50  cc.  M/5  KHPhthalate        9.90  cc.  M/5  HC1  Dilute  to  200  cc. 

3.6      50  cc.  M/5  KHPhthalate        5 .97  cc.  M/5  HC1  Dilute  to  200  cc. 

3.8      50  cc.  M/5  KHPhthalate        2.63  cc.  M/5  HC1  Dilute  to  200  cc. 

Phthalate-NaOH  mixtures 


4.0  50  cc.  M/5  KHPhthalate  0.40  cc.  M/5  NaOH  Dilute  to  200  cc. 

4.2  50  cc.  M/5  KHPhthalate  3.70  cc.  M/5  NaOH  Dilute  to  200  cc. 

4.4  50  cc.  M/5  KHPhthalate  7.50  cc.  M/5  NaOH  Dilute  to  200  cc. 

4.6  50  cc.  M/5  KHPhthalate  12.15  cc.  M/5  NaOH  Dilute  to  200  cc. 

4.8  50  cc.  M/5  KHPhthalate  17.70  cc.  M/5  NaOH  Dilute  to  200  cc. 

5.0  50  cc.  M/5  KHPhthalate  23.85  cc.  M/5  NaOH  Dilute  to  200  cc. 

5.2  50  cc.  M/5  KHPhthalate  29.95  cc.  M/5  NaOH  Dilute  to  200  cc. 

5.4  50  cc.  M/5  KHPhthalate  35.45  cc.  M/5  NaOH  Dilute  to  200  cc. 

5.6  50  cc.  M/5  KHPhthalate  39.85  cc.  M/5  NaOH  Dilute  to  200  cc. 

5.8  50  cc.  M/5  KHPhthalate  43.00  cc.  M/5  NaOH  Dilute  to  200  cc. 

6.0  50  cc.  M/5  KHPhthalate  45.45  cc.  M/5  NaOH  Dilute  to  200  cc. 

6.2  50  cc.  M/5  KHPhthalate  47.00  cc.  M/5  NaOH  Dilute  to  200  cc. 


STANDARD    BUFFER    SOLUTIONS 


107 


KH2P04-NaOH  mixtures 


5.8 
6.0 

6.2 
6.4 
6.6 
6.8 

7.0 
7.2 
7.4 
7.6 
7.8 
8.0 


50  cc 
50  cc 
50  cc 
50  cc, 
50  cc 
50  cc, 
50  cc, 
50  cc, 
50  cc 
50  cc, 
50  cc, 
50  cc 


M/5  KH2P04 
M/5  KH2P04 
M/5  KH2P04 
M/5  KH2P04 
M/5  KH2P04 
M/5  KH2P04 
M/5  KH2P04 
M/5  KH2P04 
M/5  KH2P04 
M/5  KH2P04 
M/5  KH2P04 
M/5  KH2P04 


3.72  cc. 

5.70  cc. 

8.60  cc. 
12.60  cc. 
17.80  cc. 
23.65  cc. 
29.63  cc. 
35.00  cc. 
39.50  cc. 
42.80  cc. 
45.20  cc. 
46.80  cc. 


M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 


Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 


to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 


Boric  acid,    KCl-NaOH  mixtures 


7.8  50  cc. 
8.0  50  cc. 
8.2  50  cc. 
8.4  50  cc. 
8.6  50  cc. 
8.8  50  cc. 
9.0  50  cc. 
9.2  50  cc. 
9.4  50  cc. 
9.6  50  cc. 
9.8  50  cc. 
10.0  50  cc. 


M/5  H3B03 
M/5  H3BO3 
M/5  H3B03 
M/5  H3B03 
M/5  H3B03 
M/5  H3B03 
M/5  H3B03 
M/5  H3B03 
M/5  H3B03 
M/5  H3B03 
M/5  H3B03 
M/5  H3B03 


M/5KC1  2 
M/5KC1  3 
M/5KC1  5 
M/5KC1  8 
M/5  KC1  12 
M/5KC1  16 
M/5  KC1  21 
M/5KC126 
M/5KC1  32 
M/5  KC1  36 
M/5  KC1  40 
M/5  KC1  43 


61  cc 
97  cc 
90  cc 
50  cc 
00  cc 
30  cc 
30  cc 
70  cc 
00  cc 
85  cc 
80  cc 
90  cc 


M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 
M/5  NaOH 


Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 


to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 
to  200  cc. 


It  is  important  to  check  the  consistency  of  any  particular  set 
of  these  mixtures  by  comparing  "5.8"  and  "6.2  phthalate"  with 
"5.8"  and  "6.2  phosphate"  using  brom  cresol  purple.  Also 
"7.8"  and  "8.0  phosphate"  should  be  compared  with  the  corre- 
sponding borates  using  cresol  red. 

S0rensen's  standards  are  made  as  follows.  The  stock  solutions 
are:  4 

1.  A  carefully  prepared  exact  tenth  normal  solution  of  HC1. 

2.  A  carbonate-free  exact  tenth  normal  solution  of  NaOH. 

3.  A  tenth  molecular  glycocoll  solution  containing  sodium  chlo- 
rid,  7.505  grams  glycocoll  and  5.85  grams  NaCl  in  1  litre  of 
solution. 

4.  An  M/15  solution  of  primary  potassium  phosphate  which 
contains  9.078  grams  KH2P04  in  1  litre  of  solution. 


108 


THE  DETERMINATION  OF  HYDROGEN  IONS 


0.C-A 


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Fia.  12.  S0rensen's  Standard  Mixtures,  Walpole's  Acetate  Solutions 

AND  PALITZSCH's  BORATE  SOLUTIONS 

Mixtures  of  A  parts  of  acid  constituent  and  B  parts  of  basic  constituent. 


STANDARD    BUFFER   SOLUTIONS  109 

5.  An  M/15  solution  of  secondary  sodium  phosphate  which 
contains  11.876  grams  Na2HP04,2H20  in  1  litre  of  solution. 

6.  A  tenth  molecular  solution  of  secondary  sodium  citrate  made 
from  a  solution  containing  21.008  grams  crystallized  citric  acid 
and  200  cc.  carbonate-free  N/1  NaOH  diluted  to  1  litre. 

7.  An  alkaline  borate  solution  made  from  12.404  grams  boric 
acid  dissolved  in  100  cc.  carbonate-free  N/1  NaOH  and  diluted 
to  1  litre. 

The  materials  for  these  solutions  are  described  by  S0rensen  as 
follows. 

The  water  shall  be  boiled,  carbon  dioxid-free,  distilled  water, 
and  the  solutions  shall  be  protected  against  contamination  by 
C02. 

Glycocoll  (Glycine) 

Two  grams  glycocoll  should  give  a  clear  solution  in  20  cc. 
water  and  should  test  practically  free  of  chlorid  or  sulfate.  Five 
grams  should  yield  less  than  2  mgm.  of  ash.  Five  grams  should 
yield,  on  distillation  with  300  cc.  of  5  per  cent  sodium  hydroxid, 
less  than  1  mgm.  of  nitrogen  as  ammonia.  The  nitrogen  content 
as  determined  by  the  Kjeldahl  method  should  be  18.67  ±0.1  per 
cent. 

Primary  phosphate,  KH2PO4 

The  salt  must  dissolve  clear  in  water  and  yield  no  test  for  chlo- 
rid or  for  sulfate.  When  dried  under  20  or  30  mm.  pressure  for 
a  day  at  100°C.  the  loss  in  weight  should  be  less  than  0.1  per  cent, 
and  on  ignition  the  loss  should  be  13.23  ±0.1  per  cent.  When 
compared  colorimetrically  with  citrate  mixtures  the  stock  phos- 
phate solution  should  lie  between  "7"  and  "8  citrate-HCl."  On 
addition  of  a  drop  of  tenth-normal  alkali  or  acid  to  100  cc.  the 
color  of  this  phosphate  solution  with  an  indicator  should  be 
widely  displaced. 

Secondary  phosphate,  Na2HP04,  2H20 

The  salt  with  this  content  of  water  of  crystallization  is  pre- 
pared by  exposing  to  the  ordinary  atmosphere  the  crystals  con- 


110  THE    DETERMINATION   OF   HYDROGEN   IONS 

taining  twelve  mols  of  water.6  About  two  weeks  exposure  is 
generally  sufficient.  The  salt  should  dissolve  clear  in  water  and 
yield  no  test  for  chlorid  or  sulfate.  A  day  of  drying  under  20  to 
30  mm.  pressure  at  100°C.  and  then  careful  ignition  to  constant 
weight,  should  result  in  a  25.28  ±  0.1  per  cent  loss.  The  stock 
solution  should  correspond  on  colorimetric  test  with  "10  borate- 
HC1"  and  should  be  displaced  beyond  "8  borate-HCl"  on  addi- 
tion of  a  drop  of  N/10  acid,  and  beyond  "8  borate-NaOH "  with 
a  drop  of  alkali  to  100  cc. 

Citric  acid,  C6H807,H20 

The  acid  should  dissolve  clear  in  water,  should  yield  no  test  for 
chlorid  or  sulfate  and  should  give  practically  no  ash.  The  water 
of  crystallization  may  be  determined  by  drying  under  20  to  30 
mm.  pressure  at  70° C.  On  drying  in  this  manner  the  acid  should 
remain  colorless  and  lose  8.58  ±  0.1  per  cent.  The  acidity  of  the 
citric  acid  solution  is  determined  by  titration  with  0.2  N  barium 
hydroxid  with  phenolphthalein  as  indicator.  Titration  is  carried 
to  a  distinct  red  color  of  the  indicator. 

Boric  acid,  H3B03 

Twenty  grams  of  boric  acid  should  go  completely  into  solution 
in  100  cc.  of  water  when  warmed  on  a  strongly  boiling  water  bath. 
This  solution  is  cooled  in  ice  water  and  the  filtrate  from  the  crys- 
tallized boric  acid  is  tested  as  follows.  It  should  give  no  tests  for 
chlorides  or  sulfates.  It  should  be  orange  to  methyl  orange.  A 
drop  of  N/10  HC1  added  to  5  cc.  should  make  the  filtrate  red 
to  methyl  orange.  Twenty  cubic  centimeters  of  the  filtrate  evap- 
orated in  platinum,  treated  with  about  10  grams  of  hydrofluoric 
acid  and  5  cc.  of  concentrated  sulfuric  acid  and  reevaporated, 
ignited  and  weighed,  should  yield  less  than  2  mgm.  when  corrected 
for  non-volatile  matter  in  the  HF. 

fne  following  tables  give  the  S0rensen  mixtures  with  the  cor- 
responding pH  values.     Mixtures  whose  pH  values  are  consid- 

•  Certain  samples  of  secondary  sodium  phosphate  sold  for  the  prepa- 
ration of  buffer  standards  and  called  "S0rensen's  Phosphate"  are  wrongly 
labeled  Na2HP04. 


STANDARD    BUFFER    SOLUTIONS 


111 


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9.0  Glycine  +  1.0  NaOH 
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7.0  Glycine  +  3.0  NaOH 

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2.0  G  lycine  +  8.0  NaOH 
1.0  G  lycine  +  9.0  NaOH 

112 


THE   DETERMINATION    OF   HYDROGEN    IONS 


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TABLE  24 
Stfrensen's  borate — HCl  mixtures  after  W album 


10° 

20° 

30° 

40° 

50° 

60° 

70° 

10.0  Borate 

9.30 
9.22 

9.23 
9.15 

9.15 

9.08 

9.08 
9.01 

9.00 
8.94 

8.93 

8.87 

8.86 

9.5  Borate  +  0.5  HCl 

8.80 

9.0  Borate  +  1.0  HCl 

9.14 

9.07 

9.01 

8.94 

8.87 

8.80 

8.74 

8.5  Borate  +  1.5  HCl 

9.06 

8.99 

8.92 

8.86 

8.80 

8.73 

8.67 

8.0  Borate  +  2.0  HCl 

8.96 

8.89 

8.83 

8.77 

8.71 

8.65 

8.59 

7.5  Borate  +  2.5  HCl 

8.84 

8.79 

8.72 

8.67 

8.61 

8.55 

8.50 

7.0  Borate  +  3.0  HCl 

8.72 

8.67 

8.61 

8.56 

8.50 

8.45 

8.40 

6.5  Borate  +  3.5  HCl 

8.54 

8.49 

8.44 

8.40 

8.35 

8.30 

8.26 

6.0  Borate  +  4.0  HCl 

8.32 

8.27 

8.23 

8.19 

8.15 

8.11 

8.08 

5.75  Borate  +  4.25  HCl... 

8.17 

8.13 

8.09 

8.06 

8.02 

7.98 

7.95 

5.5  Borate  +  4.5  HCl 

7.96 

7.93 

7.89 

7.86 

7.82 

7.79 

7.76 

5.25  Borate  +  4.75  HCl... 

7.64 

7.61 

7.58 

7.55 

7.52 

7.49 

7.47 

TABLE    25 
Sflrensen's  citrate — NaOH  mixtures  after  Walbum 


Temperature. 


10.0  Citrate 

9.5  Citrate  +  0.5  NaOH.. 
9.0  Citrate  +  1.0  NaOH.. 
8.0  Citrate  +  2.0  NaOH.. 
7.0  Citrate  +  3.0  NaOH.. 
6.0  Citrate  +  4.0  NaOH.. 
5.5  Citrate  +  4.5  NaOH.. 
5.25  Citrate  +  4.75  NaOH 


10° 

20° 

30° 

4C° 

50° 

60° 

4.93 

4.96 

5.00 

5.04 

5.07 

5.10 

4.99 

5.02 

5.06 

5.10 

5.13 

5.16 

5.08 

5.11 

5.15 

5.19 

5.22 

5.25 

5.27 

5.31 

5.35 

5.39 

5.42 

5.45 

5.53 

5.57 

5.60 

5.64 

5.67 

5.71 

5.94 

5.98 

6.01 

6.04 

6.08 

6.12 

6.30 

6.34 

6.37 

6.41 

6.44 

6.47 

6.65 

6.69 

6.72 

6.76 

6.79 

6.83 

70° 


5.14 
5.20 
5.29 
5.49 
5.75 
6.15 
6.51 
6.86 


TABLE  26 
irensen's  glycocoll — HCl  mixtures 


GLYCOCOLL 

HCl 

pH 

CC.                              , 

CC. 

0.0 

10.0 

1.038 

1.0 

9.0 

1.146 

2.0 

8.0 

1.251 

3.0 

7.0 

1.419 

4.0 

6.0 

1.645 

5.0 

5.0 

1.932 

6.0 

4.0 

2.279 

7.0 

3.0 

2.607 

8.0 

2.0 

2.922 

9.0 

1.0 

3.341 

9.5 

.     0.5 

3.679 

113 


114 


THE   DETERMINATION   OF   HYDROGEN   IONS 


TABLE  27 

irensen's  phosphate  mixtures 


SECONDARY 

PRIMARY 

pH 

CC. 

CC. 

0.25 

9.75 

5.288 

0.5 

9.5 

5.589 

1.0 

9.0 

5.906 

2.0 

8.0 

6.239 

3.0 

7.0 

6.468 

4.0 

6.0 

6.643 

5.0 

5.0 

6.813 

6.0 

4.0 

6.979 

7.0 

3.0 

7.168 

8.0 

2.0 

7:381 

9.0 

1.0 

7.731 

9.5 

0.5 

8.043 

TABLE  28 
S0rensen's  citrate — HCl  mixtures 


CITRATE 

HCl 

pH 

CC. 

CC. 

0.0 

10.0 

1.038 

1.0 

9.0 

1.173 

2.0 

8.0 

1.418 

3.0 

7.0 

1.925 

3.33 

6.67 

2.274 

4.0 

6.0 

2.972 

4.5 

5.5 

3.364 

4.75 

5.25 

3.529 

5.0 

5.0 

3.692 

5.5 

4.5 

3.948 

6.0 

4.0 

4.158 

7.0 

3.0 

4.447 

8.0 

2.0 

4.652 

9.0 

1.0 

4.830 

9.5 

0.5 

4.887 

10.0 

0.0 

4.958 

STANDARD    BUFFER   SOLUTIONS 


115 


TABLE  29 

Walpole's  acetate  buffer  mixtures,  recalculated  for  intervals  of  0.2  pH. 
acetate  0.2  molecular 


Total 


PH 

CONCENTRATION    (MOLALITY) 

Acetic  Acid 

Sodium  acetate 

3.6 
3.8 

4.0 
4.2 
4.4 
4.6 
4.8 
5.0 
5.2 
5.4 
5.6 

0.185 
0.176 
0.164 
0.147 
0.126 
0.102 
0.080 
0.059 
0.042 
0.029 
0.019 

0.015 
0.024 
0.036 
0.053 
0.074 
0.098 
0.120 
0.141 
0.158 
0.171 
0.181 

TABLE  30 

Palitzsch's  borax-boric  acid  mixtures 


M/20   BORAX 

M/5  boric  acid,  M/20  NaCl 

pH 

cc. 

cc. 

10.0 

0.0 

9.24 

9.0 

1.0 

9.11 

8.0 

2.0 

8.98 

7.0 

3.0 

8.84 

6.0 

4.0 

8.69 

5.5 

4.5 

8.60 

5.0 

5.0 

8.51    ' 

4.5 

5.5 

8.41 

4.0 

6.0 

8.31 

3.5 

6.5 

8.20 

3.0 

7.0 

8.08 

2.5 

7.5 

7.94 

2.3 

7.7 

7.88 

2.0 

8.0 

7.78 

1.5 

8.5 

7.60 

1.0 

9.0 

7.36 

0.6 

9.4 

7.09 

0.3 

9.7 

6.77 

116 


THE  DETERMINATION  OF  HYDROGEN  IONS 


ered  by  S0rensen  to  be  too  uncertain  and  which  he  has  indicated 
by  brackets  are  omitted  in  these  tables.  The  third  decimal  of 
S0rensen's  tables  are  given  by  S0rensen  in  small  type. 


TABLE  31 
Mcllvaine's  standards 


pH  REQUIRED 

0.2MNa2HPO< 

0.1  M  CITRIC  ACID 

cc. 

CC. 

2.2 

0.40 

19.60 

2.4 

1.24 

18.76 

2.6 

2.18 

17.82 

2.8 

3.17 

16.83 

3.0 

4.11 

15.89 

3.2 

4.94 

15.06 

3.4 

5.70 

14.30 

3.6 

6.44 

13.56 

3.8 

7.10 

12.90 

4.0 

7.71 

12.29 

4.2 

8.28 

11.72 

4.4 

8.82 

11.18 

4.6 

9.35 

10.65 

4.8 

9.86 

10.14 

5.0 

10.30 

9.70 

5.2 

10.72 

9.28 

5.4 

11.15 

8.85 

5.6 

11.60 

8.40 

5.8 

12.09 

7.91 

6.0 

12.63 

7.37 

6.2 

13.22 

6.78 

6.4 

13.85 

6.15 

6.6 

14.55 

5.45 

6.8 

15.45 

4.55 

7.0 

16.47 

3.53 

7.2 

17.39 

2.61 

7.4 

18.17 

1.83 

7.6 

18.73 

1.27 

7.8 

19.15 

0.85 

8.0 

19.45 

0.55 

Walbum  (1920)  has  determined  the  pH  values  for  the  S0ren- 
sen  mixtures  at  temperatures  of  10°,  18°,  28°,  37°,  46°,  62°  and 
70°C.  and  has  interpolated  data  for  intervening  temperatures. 
He  uses  a  system  of  reference  essentially  that  which  is  described 


STANDARD    BUFFER   SOLUTIONS  117 

in  Chapter  XIX  as  standard.  He  finds  that  upon  this  basis  the 
alteration  of  pH  with  temperature  is  for  the  most  part  negligible 
for  the  phosphate  mixtures,  the  glycocoll-HCl  mixtures  and  the 
citrate-HCl  mixtures.  Data  for  the  other  mixtures  are  tabu- 
lated in  tables  22,  23,  24  and  25.  In  these  will  be  found  S0ren- 
sen's  values  at  18°.  Tables  26,  27  and  28  are  taken  from 
S0rensen's  paper  of  1912. 

The  stock  solutions  for  the  Palitzsch  mixtures  given  in  table  30 
are  an  M/20  Borax  solution  containing  19.108  grams7  Na2B407 
10H2O  in  1  litre;  and  an  M/5  Boric  acid,  NaCl  solution  contain- 
ing 12.404  grams7  H3B03  and  2.925  grams  NaCl  in  1  litre. 

Mcllvaine  (1921)  has  given  the  electrometrically  determined 
pH  values  for  a  series  of  mixtures  of  0.2  M  disodium  phosphate 
and  0.1  M  citric  acid.  Since  the  citrate  exerts  a  buffer  action 
at  the  steep  part  of  the  phosphate  curve  near  the  position  where 
the  mono  alkali  phosphate  alone  is  present  Mcllvaine's  mixtures 
give  a  continuous  buffer  action  from  pH  2.2  to  pH  8.0.  His  data 
are  shown  in  table  31. 

Acree  and  his  coworkers  have  published  curves  for  other  mix- 
tures giving  more  or  less  smooth  slopes  over  wide  ranges  of  pH. 

Kolthoff  in  his  1921  text  has  recalculated  the  follow, ing  data 
from  Ringer  (1909): 

TABLE  32 
Ringer's  mixtures  of  0.15M  Na2HPOi  and  0.1M  NaOH 


50  cc.  Na2HP04  +  15  cc.  NaOH. 
50  cc.  Na2HP04  +  25  cc.  NaOH. 
50  cc.  Na2HP04  +  50  cc.  NaOH. 
50  cc.  Na2HP04  +  75  cc.  NaOH. 


pH 


10.97 
11.29 
11.77 
12.06 


7  The  values  given  by  Palitzsch  were  calculated  upon  the  basis  of  11.0 
as  the  atomic  weight  of  boron.  Since  this  was  the  value  used,  the  new 
value  of  10.9  given  in  the  atomic  weight  table  in  1  he  report  of  the  inter- 
national committee  for  1922  should  not  be  used  in  calculating  the  composi- 
tion of  the  specific  solutions  given  by  Palitzsch. 


CHAPTER  VII 

Sources  of  Error  in  Colorimetric  Determinations 

There  are  errors  of  technique  such  as  incorrect  apportionment 
of  the  indicator  concentration  in  tested  and  standard  solution  and 
the  use  of  unequal  depths  of  solutions  through  which  the  colors 
are  viewed  that  may  be  passed  over  with  only  a  word  of  reminder. 
Likewise  we  may  recall  certain  of  the  optical  effects  mentioned 
in  Chapter  IV  and  then  pass  on  to  the  more  serious  difficulties 
in  the  application  of  the  indicator  method. 

In  the  comparison  of  electrometric  and  colorimetric  measure- 
ments discrepancies  have  often  been  traced  so  clearly  to  two  defi- 
nite sources  of  error  that  they  have  been  given  categorical  dis- 
tinction.    They  are  the  so-called  "protein"  and  "salt"  errors. 

From  what  has  already  been  said  in  previous  pages,  it  will 
be  seen  that,  if  there  are  present  in  a  tested  solution  bodies  which 
remove  the  indicator  or  its  ions  from  the  field  of  action  either  by 
adsorption ,  or  otherwise,  the  equilibria  which  have  formed  the 
basis  of  our  treatment  will  be  disturbed.  An  indicator  in  such  a 
solution  may  show  a  color  intensity,  or  even  a  quality  of  color, 
which  is  different  from  that  of  the  same  concentration  of  the  indi- 
cator in  a  solution  of  the  same  hydrogen  ion  concentration  where 
no  such  disturbance  occurs.  We  could  easily  be  led  to  attribute 
very  different  hydrogen  ion  concentrations  to  the  two  solutions. 
This  situation  is  not  uncommon  when  we  are  dealing  with  protein 
solutions,  for  in  some  instances  there  is  distinctly  evident  the  re- 
moval of  the  indicator  from  the  field.  In  other  cases  the  discrep- 
ancy between  electrometric  and  colorimetric  measurements  is  not 
so  clear,  nor  can  it  always  be  attributed  solely  to  the  indicator 
measurement. 

If  two  solutions  of  inorganic  material,  each  containing  the  same 
concentration  of  hydrogen  ions,'  are  tested  with  an  indicator,  we 
should  expect  the  same  color  to  appear.  If,  however,  these  two 
solutions  have  different  concentrations  of  salt,  it  may  happen  that 
the  indicator  color  is  not  the  same.  As  S0rensen  (1909)  and 
Scfrensen  and  Palitzsch  (1913)  have  demonstrated,  this  effect  of 

118 


ERRORS   IN    COLORIMETR1C    DETERMINATIONS 


119 


the  salt  content  of  a  solution  cannot  be  tested  by  adding  the  salt 
to  one  of  two  solutions  which  have  previously  been  brought  to 
the  same  hydrogen  ion  concentration.  The  added  salt,  no  matter 
if  it  be  a  perfectly  neutral  salt,  will  change  either  the  hydrogen 
ion  concentration  or  the  hydrogen  ion  activity  of  the  solution  or 
so  affect  the  electrode  equilibrium  that  it  appears  as  if  the  hydro- 
gen ion  activity  is  altered. 

So  long  as  hydrogen  electrode  measurements  are  made  the 
standard  it  is  convenient  to  throw  the  burden  of  the  "salt  effect" 
upon  the  indicator;  but  neutral  salts  are  known  to  displace  elec- 
trode potential  differences  from  the  point  estimated  from  the 
expected  hydrogen  ion  concentration.  Tentatively  we  may  deal 
with  the  salt  effect  as  if  the  hydrogen  electrode  measurement 
were  the  point  of  reference,  and  this  will  doubtless  harmonize 
with  future  developments  of  theory. 

Bjerrum  (1914)  gives  an  example  of  a  case  where  the  influence 
}f  the  neutral  salt  is  evidently  upon  the  buffer  equilibrium  rather 
;han  on  the  indicator.  An  ammonium-ammonium  salt  buffer 
nixture  and  a  borate  buffer  mixture  are  both  made  up  to  the 
name  color  of  phenolphthalein.  On  the  addition  of  sodium  chlo- 
ride the  color  of  phenolphthalein  becomes  stronger  in  the  ammo- 
nium mixture  and  weaker  in  the  borate  mixture. 

The  following  table  taken  from  Prideaux  (1917)  illustrates  the 
order  of  magnitude  of  the  "salt  error"  in  some  instances. 


INDICATOR 


]  ara  benzene  sulphonic  acid  azo  naphthylamine. 

I  ara  nitro  phenol 

/  lizarine   sulphonic  acid 

1  eutral  red 

I  osolic  acid 

I  ara  benzene  sulphonic  acid  azo  a-naphthol  . . . 
I  henolphthalein 


BUFFER   USED 


Phosphate 
Phosphate 
Phosphate 
Phosphate 
Phosphate 
Phosphate 
Phosphate 


CHANGE  OF  pH 

IN  PRESENCE  OF 

0.5  N  NaCl 


-0.10 
+0.15 
+0.26 
-0.09 
+0.08 
+0.12 
+0.12 


\  In  cases  where  the  solutions  under  examination  are  of  the  same 
g  meral  nature  hydrogen  electrode  measurements  may  be  taken  as 
t  te  standard  and  colorimetric  measurements  calibrated  accord- 
i  gly.     S0rensen  and  Palitzsch  (1910)  did  this  in  their  study  of 


120 


THE  DETERMINATION  OF  HYDROGEN  IONS 


the  salt  errors  of  indicators  in  sea  water.  They  acidified  the  sea 
water  and  passed  hydrogen  through  to  displace  carbon  dioxid, 
and  then  neutralized  it  to  the  ranges  of  various  indicators  with 
buffer  mixtures  and  compared  colorimetric  with  electrometric 
measurements.     In  this  way  they  found  the  following  deviations. 


INDICATOR 

BUFFER 

PARTS   PER    1000   OF  SALTS   AND 
CORRESPONDING  ERRORS 

35 

20 

5 

l 

Faranitro  phenol 

Phosphate 

Phosphate 

Borate 

Phosphate 

Borate 

+0.12 
-0.10 
+0.22 
+0.16 
+0.21 

+0.08 
-0.05 
+0.17 
+0.11 
+0.16 

0 

+0.03 
-0.04 
+0.05 

Neutral  red 

0 

a-Napththol  phthalein..\ 
Phenolphthalein 

-0.07 
-0.14 
-0.03 

If,  for  example,  sea  water  of  about  3.5  per  cent  salt  is  matched 
against  a  standard  borate  solution  with  phenolphthalein  and 
appears  to  be  pH  8.43  the  real  value  is  pH  8.22. 

Such  calibration  is  doubtless  the  very  best  way  to  deal  with  the 
salt  errors  since  it  tends  to  bring  measurements  to  a  common 
experimental  system  of  reference. 

Kolthoff  (1922)  gives  the  following  table  showing  the  correc- 
tions to  be  applied  for  the  "salt  error"  of  various  indicators.  It 
should  be  noted  that  Kolthoff  includes  in  this  table  data  obtained 
when  the  hydrogen  electrode  potentials  were  taken  as  standard 
and  also  data  in  which  the  pH  values  were  calculated.  The  two 
sets  are  not  strictly  comparable  (see  Chapter  XIX)  and  there- 
fore must  be  used  with  caution  in  theoretical  work.  We  have 
eliminated  from  Kolthoff's  table  Congo  red,  Azolitmin,  and 
Tropaeolin  O  (Chrysom)  which  Kolthoff  describes  as  having 
salt  errors  so  large  that  these  indicators  are  useless. 

Michaelis  and  his  coworkers  have  determined  the  salt  errors 
for  a  number  of  the  nitrophenols,  but,  since  the  corrections  are 
often  intimately  related  to  the  constants  used  in  Michaelis* 
method  of  operating,  the  reader  is  referred  to  the  original  litera- 
ture for  the  details.    See  Chapter  VIII. 

The  reader  was  warned  in  Chapter  II  that  the  treatment  to  be 
given  the  so-called  salt  errors  of  indicators  would  not  deal  with  the 
theory.    There  are  various  theories  that  have  been  advanced, 


TABLE    33 

Salt  error  of  indicators,  after  Kolthoff 


INDICATOR 


Tropaeolin  00 
(Orange  IV) 


Methyl  orange 
Butter  yellow. . 


Thymol  blue  (acid 
range) 


Brom  phenol  blue  < 

Brom  cresol  purple. 
Phenol  red 


Thymol  blue 

Methyl  red 

p-Nitro  phenol.. . 
Azo  yellow  3G. . . 
Phenolph  thalein . 

Nitramine  (?)... 


SALT 

SALT 
CONCEN- 
TRATION 

CORREC- 
TION 

KC1 

0.10  N 

-0.05 

KC1 

0.25  N 

-0.01 

KC1 

0.50  N 

+0.06 

KC1 

1.00  N 

+0.23 

KC1 

0.10  N 

-0.08 

KC1 

0.25  N 

-0.08 

KC1 

0.50  N 

+0.02 

KC1 

1.00  N 

+0.23 

KC1 

0.10  N 

-0.08 

KC1 

0.10  N 

-0.06 

KC1 

0.20  N 

-0.06 

KC1 

0.50  N 

-0.04 

KC1 

1.00  N 

+0.05 

KC1 

0.10  N 

-0.05 

KC1 

0.25  N 

-0.15 

KC1 

0.50  N 

-0.35 

KC1 

1.00  N 

-0.35 

NaCl 

0.50  N 

-0.25 

NaCl 

0.50  N 

-0.15 

NaCl 

0.50  N 

-0.17 

NaCl 

0.50  N 

+0.10 

NaCl 

0.50  N 

-0.05 

NaCl 

0.50  N 

0.00 

NaCl 

0.50  N 

-0.17 

KC1 

0.10  N 

-0.06 

KC1 

0.25  N 

-0.12 

KC1 

0.50  N 

-0.10 

KC1 

1.00  N 

-0.29 

REMARKS 


Indicator    suitable.      NaCl 
has  about  same  influence 


Indicator     suitable.     NaCl 
has  about  same  influence 


Same  errors  as  methyl 
orange  but  indicator  floc- 
culates with  salt 

NaCl  has  same  influence 


Corrections  large  at  weaker 
concentration  of  salt 


At  small  concentrations  of 
salt  correction  of  opposite 
sign 


NaCl  has  about  same  influ- 
ence 


121 


122  THE   DETERMINATION   OF   HYDROGEN   IONS 

but  up  to  a  recent  time  none  has  been  entirely  satisfactory. 
Whether  the  newer  concepts  of  the  conduct  of  strong  electrolytes 
will  furnish  a  basis  for  the  correlation  of  experimental  data  remains 
to  be  seen.  This  much  at  least  will  be  demanded,  that  the  habit 
of  indiscriminately  jumbling  together  dissociation  constants  and 
other  data  obtained  by  widely  different  methods  and  bearing 
different  implications  shall  cease.  Until  a  thoroughly  consistent 
method  of  approach  and  of  calculation  is  accomplished  and  its 
value  established,  the  only  safe  procedure  to  follow  is  to  calibrate 
salt  errors  by  experimental  hydrogen  electrode  measurements. 

In  dealing  with  protein  solutions  calibration  is  less  certain. 
When  solutions  to  be  tested  vary  greatly,  not  only  in  protein  con- 
tent but  also  in  the  composition  and  concentration  of  their  salt 
content,  systematic  calibration  becomes  very  difficult.  When 
there  are  added  the  difficulties  presented  by  strong  coloration 
and  turbidity,  calibration  is  impossible.  Such  is  the  situation  to 
be  faced  when  dealing  with  the  media  and  the  cultures  which 
the  bacteriologist  must  handle. 

It  is  sometimes  helpful  to  construct  titration  curves  of  a  solu- 
tion under  examination,  making  measurements  after  addition  of 
graded  quantities  of  acid  and  alkali,  in  one  case  with  the  hydrogen 
electrode  and  in  the  other  case  with  indicators,  preferably  indi- 
cators of  different  types.  The  indicator  readings  may  then  reveal 
breaks  not  to  be  expected  from  the  hydrogen  ion  relations  of  the 
solution.  If,  however,  no  comparison  is  made  with  hydrogen 
electrode  measurements,  the  observer  must  rely  to  a  considerable 
extent  upon  his  judgment.  "Protein  errors"  are  generally  the 
larger  the  more  complex  and  concentrated  the  protein  and  tend 
to  decrease  with  increase  in  the  extent  of  protein  hydrolysis. 

There  seems  to  be  no  way  then  to  deal  with  either  the  protein 
or  the  salt  error  of  indicators  but  to  rely  upon  the  use  of  those 
indicators  which  give  relatively  small  errors,  to  keep  in  mind  the 
order  of  magnitude  of  the  error  to  be  expected  from  the  general 
nature  of  the  solution  tested,  and,  in  important  cases,  to  standard- 
ize to  the  electrometric  basis  as  an  arbitrary  provisional  standard. 

Because  of  the  great  variety  of  solutions  tested  by  the  colori- 
metric  method  it  is  impracticable  to  give  a  condensed  statement 
of  the  probable  errors.  Elaborate  tables  of  colorimetric  and 
electrometric  comparisons  are  given  by  S0rensen  (1909)  for  the 


ERRORS   IN    COLORIMETRIC    DETERMINATIONS  123 

cases  he  studied.  Clark  and  Lubs  (1917)  have  tabulated  their 
results  with  the  sulphonphthalein  indicators. 

In  the  work  of  Michaelis  or  that  of  Kolthoff  salt  corrections 
are  for  the  most  part  established  by  means  of  hydrogen  electrode 
measurements.  Wells  (1920)  has  tabulated  some  data  for  cresol 
red  in  a  manner  useful  for  a  certain  type  of  water  study  (cf.  Mc- 
Clendon  1917),  and  Brightman,  Meacham  and  Acree  (1920)  have 
recorded  the  effects  of  different  concentrations  of  phosphate 
buffer. 

The  "protein  error"  and  the  "salt  error"  have  been  given 
prominence  in  the  literature  partly  because  both  have  to  be  taken 
into  consideration  in  dealing  with  biological  solutions,  and  partly 
because  there  is  to  be  perceived  underlying  the  salt  error  a  most 
interesting  phenomenon  of  rather  general  interest.  However, 
this  emphasis  should  not  obscure  the  fact  that  there  are  specific 
conditions  for  each  indicator  which  render  that  indicator  useless 
for  the  determination  of  pH.  For  instance  alizarine,  in  passing 
from  the  phosphate  to  the  borate  buffer  mixtures  exhibits  a  sudden 
transition  which  has  all  the  appearances  of  a  specific  effect  of  the 
borate  upon  the  indicator.  And  alizarine  is  not  alone  in  this 
peculiarity.  This  same  alizarine  in  the  presence  of  aluminium 
may  form  a  lake  and  with  proper  pH  control  may  be  made  a  use- 
ful reagent  for  aluminium  in  place  of  a  very  poor  acid-base  indica- 
tor. Zoller  (1921)  has  called  attention  to  the  incompatibility 
between  certain  dyes  and  the  phthalate  buffers.  Many  indica- 
tors are  easily  reduced  or  like  methyl  red  easily  reduced  and  then 
so  altered  that  the  reduction  is  irreversible.  A  number  of  indi- 
cators undergo  their  color  changes  slowly  or  else  fade  and  are 
lost  to  the  observer.  Other  indicators  precipitate  with  certain 
cations,  for  instance  Orange  IV  and  Congo  with  alkali  earths. 
In  short  all  possibilities  must  be  watched  lest  the  investigator, 
venturing  upon  the  study  of  some  new  solution,  be  misled  by  the 
mark  of  reliability  placed  upon  an  indicator  tried  under  limited 
circumstances. 

Wherever  possible  it  is  good  practice  to  test  doubtful  cases 
with  two  indicators  of  widely  different  chemical  composition. 

As  to  the  effect  of  temperature  variation,  comparatively  little 
work  has  been  done.  Gillespie  and  others  have  some  notes  on 
the  subject  and  more  recently  Michaelis  and  his  coworkers  have 


124 


THE   DETERMINATION   OF   HYDROGEN   IONS 


included  temperature  data  in  stating  the  constants  used  in  the 
Michaelis  and  Gyemant  method  (see  Chapter  VIII).  Kolthoff 
(1921)  has  extended  the  theory  of  School  in  which  account  is 
taken  of  the  acidic  or  basic  nature  of  an  indicator,  but  there  often 
remains  some  question  as  to  how  a  given  indicator  is  to  be  classi- 
fied. Kolthoff  using  the  values  of  Kohlrausch  and  Heydweiller 
for  the  dissociation  constant  of  water  at  various  temperatures 
has  reduced  his  observations  to  the  following  table.     In  this 


TABLE  34 
Displacement  of  indicator  exponent  between  18°C.  and  70°C.  after  Kolthoff 


INDICATOR 


Nitramine 

Phenol  phthalein 

Thymol  blue,  alkaline  range 

a-naphthol  phthalein 

Curcumine 

Phenol  red 

Neutral  red 

Brom  cresol  purple. 

Azolitmin 

Methyl  red 

Lacmoid 

p-nitro  phenol 

Methyl  orange 

Butter  yellow 

Bromphenol  blue 

Tropaeolin  00 

Thymol  blue,   acid  range . . 


pH  DIS- 
PLACEMENT 


-1.45 
-0.9  to  0.4 
-0.4 
-0.4 
-0.4 
-0.3 
-0.7 

0.0 

0.0 
-0.2 
-0.4 
-0.5 
-0.3 
-0.18 

0.0 
-0.45 

0.0 


pOH  DISPLACE- 
MENT 


0.0 
-0.55  to  1.05 
-1.05 
-1.05 
-1.05 
-1.15 
-0.75 
-1.45 
-1.45 
-1.25 
-1.05 
-0.95 
-1.15 
-1.17 
-1.45 
-1.0 
-1.45 


RATIO  OF 
DISSOCIATION 
CONSTANT  AT 

70°C.  TO  THAT 
AT  ORDINARY 

TEMPERATURE 


1.0 
About  5 
2.5 
2.5 
2.5 
2.0 

1.0 
1.0 

2.5 

3.2 
14.0 
15.0 

1.0 
10.0 

1.0 


table  the  displacement  of  —0.4  for  thymol  blue  means  that  if 
thymol  blue  in  a  solution  at  70°C.  shows  the  same  color  as  the 
same  concentration  of  this  indicator  in  a  buffer  of  pH  9.4  at 
ordinary  temperature  then  the  pH  of  the  solution  at  70°C.  is  9.0. 
Corrections  for  temperatures  between  room  temperature  and 
70CC.  may  be  interpolated  from  the  data  in  the  table. 


ERRORS  IN  COLORIMETRIC  DETERMINATIONS        125 

REFERENCES 

Abegg-Bose  (1899),  Arrhenius  (1899),  Bjerrum  (1914),  Brightman-Meacham 
Acree  (1920),  Chow  (1920),  Clark-Lubs  (1917),  Dawson-Powis  (1913), 
Gillespie-Wise  (1918),  Harned  (1915),  Kolthoff  (1916,  1918,  1922), 
Lewis  (1912),  McBain-Coleman  (1914),  McBain-Salmon  (1920), 
Michaelis  (1920-21),  Michaelis-Gyemant  (1920),  Michaelis-Kruger 
(1921),  Michaelis-Rand  (1909),  Palmaer-Melander  (1915),  Poma 
(1914),  Poma-Patroni  (1914),  Prideaux  (1917),  Rosenstein  (1912), 
Sackur  (1901),  SpTensen  (1909),  S0rensen-Palitzsch  (1910),  (1913), 
Wells  (1920),  Zoller  (1921). 
See  also  Chapter  II  and  page  341. 


CHAPTER  VIII 
Approximate  Determinations  with   Indicators 

If  you  can  measure  that  of  which  you  speak,  and  can  express  it  by 
a  number,  you  know  something  of  your  subject;  but  if  you  cannot 
measure  it,  your  knowledge  is  meagre  and  unsatisfactory. — Lord 
Kelvin 

The  distinctive  advantages  of  the  indicator  method  are  the 
ease  and  the  rapidity  with  which  the  approximate  hydrogen  ion 
concentration  of  a  solution  may  be  measured.  The  introduction 
of  improved  indicators,  the  charting  of  their  pH  ranges,  better 
definition  of  degree  in  "acidity"  or  "alkalinity,"  and  the  illumina- 
tion of  the  theory  of  acid-base  equilibria  have  developed  among 
scientific  men  in  general  an  appreciation  of  how  indefinite  were 
those  old,  favorite  terms — "slightly  acid,"  "distinctly  alkaline," 
and  "neutral."  There  is  now  a  clear  recognition  of  the  distinct 
difference  between  quantity  and  intensity  o'f  acidity;  and  for 
each  aspect  there  may  be  given  numerical  values  admitting 
no  misunderstanding. 

Furthermore  the  clarification  of  the  subject  has  brought  a 
perspective  which  may  show  where  accuracy  is  unnecessary  and 
where  fair  approximation  is  desirable.  In  such  a  case  the  investi- 
gator turns  to  the  indicator  method  knowing  that  even  if  his 
results  are  rough  they  can  still  be  expressed  in  numerical  values 
having  a  definite  meaning  to  others. 

Now  a  very  good  approximation  may  be  attained  by  color 
memory  and  without  the  aid  of  the  standard  buffer  solutions 
or  of  the  systems  presently  to  be  described  in  which  the  standard 
buffer  solutions  are  dispensed  with. 

To  establish  a  color  memory  as  well  as  to  refresh  it  a  set  of 
"permanent"  standards  is  convenient.  These  may  be  prepared 
with  the  standard  buffer  solutions  in  the  ordinary  way,  protected 
against  mold  growth  by  means  of  a  drop  of  toluol,  and  sealed 
by  drawing  off  the  test  tubes  in  a  flame  or  by  corking  with  the 
cork  protected  by  tinfoil  or  paraffme.  For  exhibition  purposes 
long  homeopathic  vials  make  a  very  good  and  uniform  container. 
They  may  be  filled  almost  to  the  brim  and  a  cork  inserted,  if  a 

126 


APPROXIMATE    INDICATOR   METHODS  127 

slit  is  made  for  the  escape  of  excess  air  and  liquid.  The  slit  may 
then  be  sealed  with  paraffine.  A  hook  of  spring-brass  snapped 
about  the  neck  makes  a  support  by  which  the  vial  may  be  fastened 
to  an  exhibition  board.  A  neater  container  is  the  so-called  typhoid- 
vaccine  ampoule  which  is  easily  sealed  in  the  flame. 

If  one  of  a  series  of  standards  so  prepared  should  alter,  the 
change  can  generally  be  detected  by  the  solution  falling  out  of 
the  proper  slope  of  color  gradation.  But  if  all  in  a  series  should 
change,  it  may  be  necessary  to  Gompare  the  old  with  new  stand- 
ards. Because  such  changes  do  occur,  "permanent"  standards 
are  to  be  used  with  caution.  The  sulfon  phthalein  indicators 
make  fairly  permanent  standards  but  the  methyl  red  which  is  an 
important  member  of  the  series  of  indicators  recommended  by 
Clark  and  Lubs  (1917)  often  deteriorates  within  a  short  time. 

A  device  which  furnishes  a  color  standard  to  be  interpreted  by 
means  of  a  dissociation  curve  is  the  color  wedge  of  Bjerrum  (1914). 
This  is  a  long  rectangular  box  with  glass  sides  and  a  diagonal  glass 
partition  which  divides  the  interior  into  two  equal  wedges.  One 
compartment  contains  a  solution  of  the  indicator  fully  transformed 
into  its  alkaline  form,  the  other  a  like  concentration  of  the  indi- 
cator transformed  to  the  acid  form.  A  view  through  these  wedges 
should  imitate  the  view  of  a  like  depth  and  concentration  of  the 
indicator  transformed  to  that  degree  which  is  represented  by  the 
ratio  of  wedge  thicknesses  at  the  point  under  observation. 
Compare  Barnett  and  Barnett  (1920)  and  Myers  (1922). 

As  an  aid  to  memory  the  dissociation  curves  of  the  indicators 
are  helpful  even  when  used  alone.  The  color  chart  shown  in 
Chapter  III  is  a  still  better  aid  to  memory  and  within  the  limita- 
tions mentioned  the  colors  may  be  used  as  rough  standards. 

Sonden  (1921)  has  used  colored  glasses  and  Kolthoff  (1922) 
inorganic  salt  solutions  as  color  standards. 

Colorimetric  determination  of  hydrogen  ion  concentration  without 
the  use  of  standard  buffer  solutions 

We  have  already  seen  that  if  an  indicator  is  an  acid,  its  degree 
of  dissociation,  a,  is  related  to  the  hydrogen  ion  concentration 
of  the  solution  by  the  equation 

[H+]  =  Ka  1-^^ 


128  THE   DETERMINATION   OF   HYDROGEN   IONS 

We  have  also  seen  that  if  Ka,  the  true  dissociation  constant 
is  replaced  by  the  so-called  apparent  dissociation  constant,  KiA, 
which  is  a  function  of  Ka  and  of  the  constants  of  tautomeric 
equilibria,  then  a  represents  the  degree  of  color  transformation. 
We  then  have 

[H+]  =  KIA^— ^ 


or  the  more  convenient  form 


pH  =  log  — -  +  log 


K     "      °1 


a 


where  a  may  now  be  considered  as  to  the  degree  of  color  trans- 
formation. If,  for  instance,  an  indicator  conducts  itself  as  a  simple 
acid  with  apparent  dissociation  constant  1  X  10~6,  we  can  con- 
struct the  dissociation  curve  with  its  central  point  of  inflection  at 
pH  6,  and  then,  assuming  that  this  curve  represents  the  relation 
of  the  percentage  color  transformation  to  pH,  we  can  determine 
the  pH  of  a  solution  if  we  can  determine  the  percentage  color 
transformation  which  this  indicator  displays  in  a  tested  solution. 
Proceeding  on  these  simple  and  often  unjustified  assumptions 
we  can  now  devise  a  very  simple  way  of  detecting  the  percentage 
color  transformation.  The  following  is  quoted  from  Gillespie 
(1920) : 

We  may  assume  that  light  is  absorbed  independently  by  the  two  forms 
of  the  indicator,  and  hence  that  the  absorption,  and  in  consequence  of  this 
the  residual  color  emerging,  will  be  the  same  whether  the  two  forms  are 
present  together  in  the  same  solution  or  whether  the  forms  are  separated 
for  convenience  in  two  different  vessels  and  the  light  passes  through  one 
vessel  after  the  other.  Therefore,  if  we  know  what  these  percentages  are 
for  a  given  indicator  in  a  given  buffer  mixture,  we  can  imitate  the  color 
shown  in  the  buffer  mixture  by  dividing  the  indicator  in  the  proper  pro- 
portion between  two  vessels,  and  putting  part  of  it  into  the  acid  form  with 
excess  of  acid,  the  rest  into  the  alkaline  form  with  excess  of  alkali. 

Gillespie  sets  up  in  the  comparator  (see  page  70)  two  tubes, 
one  of  which  contains,  for  example,  three  drops  of  a  given  indicator 
fully  transformed  into  the  acid  color,  and  the  other  of  which  con- 
tains seven  drops  of  the  indicator  fully  transformed  into  the  alka- 
line form.  The  drop  ratio  3 : 7  should  correspond  to  the  ratio  of 
the  concentrations  of  acid  and  alkaline  forms  of  ten  drops  of  the 


APPROXIMATE    INDICATOR   METHODS  129 

indicator  in  a  solution  of  that  pH  which  is  shown  by  the  disso- 
ciation curve  of  the  indicator  to  induce  a  seventy  per  cent  trans- 
formation. If  then  the  two  comparison  tubes  and  the  tested 
solution  are  kept  at  the  same  volume,  and  the  view  is  through 
equal  depths  of  each,  a  matching  of  colors  should  occur  between 
the  virage  of  the  two  superposed  comparison  tubes  and  that  of 
the  tested  solution. 

Barnett  and  Chapman  (1918)  applied  this  method  with 
one  indicator  phenol  red  but  without  using  the  dissociation 
curve.  Gillespie  (1920)  extended  the  procedure  to  several  other 
indicators  and  made  use  of  the  dissociation  curves  so  that  he 
was  able  to  smooth  out  to  more  probable  values  the  experimental 
data  relating  drop  ratios  to  pH.  This  is  important  because 
the  experimental  error  in  judging  color  is  not  inconsiderable 
and  if  the  purely  empirical  data  be  made  the  sole  basic  standardi- 
zation of  the  method  there  may  be  involved  a  systematic  error, 
which,  added  to  the  error  of  the  individual  measurement  may 
make  the  cumulative  error  unnecessarily  large.  That  this  had 
already  occurred  was  indicated  by  Gillespie's  comparison  of 
the  values  for  the  drop  ratios  of  phenol  red  given  by  Barnett  and 
Chapman  on  the  one  hand  and  the  report  of  the  bacteriologists' 
committee  (Conn,  et  al.,  1919)  on  the  other  hand. 

Gillespie  found  the  correspondence  between  the  experimental 
and  the  theoretical  results  predicted  on  the  basis  of  the  simpli- 
fying assumptions  mentioned  above  to  be  very  good  for  the  sul- 
fon  phthaleins,  doubtless  because  of  the  reasons  mentioned  in 
Chapter  IV.  He  also  showed  good  correspondence  in  the  case 
of  methyl  red  but  reiterates  the  fact  that  phenol  phthalein  cannot 
be  treated  by  means  of  the  simple  dissociation  curve  for  a  mono 
acidic  acid,  as  was  mentioned  in  Chapter  IV. 

In  table  35  are  given  the  pH  values  corresponding  to  various 
drop  ratios  of  seven  indicators  as  determined  by  Gillespie.  At 
the  bottom  of  the  table  are  shown  the  quantities  of  acid  used  to 
obtain  the  acid  color  in  each  case.  The  use  of  acid  phosphate  in- 
stead of  hydrochloric  acid  in  two  cases  is  because  the  stronger 
acid  might .  transform  the  indicator  into  that  red  form  which 
occurs  with  all  the  sulfon  phthalein  indicators  at  very  high  acidi- 
ties. The  0.05  M  HC1  is  prepared  with  sufficient  accuracy  by 
diluting  1  cc.  concentrated  hydrochloric  acid  (specific  gravity  1.19) 
to  240  cc. 


130 


THE  DETERMINATION  OF  HYDROGEN  IONS 


The  alkaline  form  of  the  indicator  is  obtained  in  each  case 
with  a  drop  of  alkali  (two  drops  in  the  case  of  thymol  blue). 
The  alkali  solution  used  for  this  purpose  may  be  prepared 
with  sufficient  accuracy  by  making  up  a  0.2  per  cent  solution 
with  ordinary  stick  NaOH.  The  indicator  solutions  may  be 
made  up  as  described  on  page  81 .  Gillespie  prefers  the  alcoholic 
solution  in  the  case  of  methyl  red  and  specifies  it  for  soil  work. 

TABLE  35 
Gillespie's  table  of  pH  values  corresponding  to  various  drop-ratios 


DROP-RATIO 

BROM- 

PHBNOL 
BLUE 

METHYL 
RED 

BROM- 
CRESOL 
PURPLE 

BROM-- 

THYMOL 

BLUE 

PHENOL 
RED 

CRESOL  RED 

THYMOL 
BLUE 

1:9 

3.1 

4.05' 

5.3 

6.15 

6.75 

7.15 

7.85 

1.5:8.5 

3.3 

4.25 

5.5 

6.35 

6.95 

7.35 

8.05 

2:8 

3.5 

4.4 

5.7 

6.5 

7.1 

7.5 

8.2 

3:7 

3.7 

4.6 

5.9 

6.7 

7.3 

7.7 

8.4 

4:6 

3.9 

4.8 

6.1 

6.9 

7.5 

7.9 

8.6 

5:5 

4.1 

5.0 

6.3 

7.1 

7.7 

8.1 

8.8 

6:4 

4.3 

5.2 

6.5 

7.3 

7  9 

8.3 

9.0 

7:3 

4.5 

5.4 

6.7 

7.5 

8.1 

8.5 

9.2 

8:2 

4.7 

5.6 

6.9 

7.7 

8.3 

8.7 

9.4 

8.5:1.5 

4.8 

5.75 

7.0 

7.85 

8.45 

8.85 

9.55 

9:1 

5.0 

5.95 

7.2 

8.05 

8.65 

9.05 

9.75 

Produce 
acid  color  < 
with 

1  cc.  of 

0.05m 

HC1 

1  drop 

of 

0.05m 

HC1 

1  drop 

of 

0.05m 

HC1 

1  drop 

of 

0.05m 

HC1 

1  drop 

of 
0.05m 
HC1 

1  drop  of 

2  per  cent 
H2KP04 

1  drop  of 

2  per  cent 
H2KPO4 

Gillespie  proceeds  as  follows: 

Test  tubes  1.5  cm.  external  diameter  and  15  cm.  long  are  suitable  for 
the  comparator  and  for  the  strengths  given  for  the  indicator  solutions.  It 
is  advisable  to  select  from  a  stock  of  tubes  a  sufficient  number  of  uniform 
tubes  by  running  into  each  10  cc.  water  and  retaining  those  which  are  filled 
nearly  to  the  same  height.  A  variation  of  3  to  4  mm.  in  a  height  of  8  cm. 
is  permissible.  Test  tubes  without  flanges  are  preferable.  The  tubes  may 
be  held  together  in  pairs  by  means  of  one  rubber  band  per  pair,  which  is 
wound  about  the  tubes  in  the  form  of  two  figure  8's. 

It  is  convenient  to  use  metal  test  tube  racks,  one  for  each  indicator, 
each  rack  holding  two  rows  of  tubes,  accommodating  one  tube  of  each  pair 
in  front  and  one  in  back.  For  any  desired  indicator  a  set  of  color  standards 
is  prepared  by  placing  from  1  to  9  drops  of  the  indicator  solution  in  the  9 
front  tubes  of  the  pairs  and  from  9  to  1  drops  in  the  back  row  of  tubes.    A 


APPROXIMATE    INDICATOR   METHODS  131 

drop  of  alkali  is  then  added  to  each  of  the  tubes  in  the  front  row  (2  drops  in 
the  case  of  thymol  blue),  sufficient  to  develop  the  full  alkaline  color  and 
a  quantity  of  acid  is  added  to  each  of  the  tubes  in  the  back  row  to  develop 
the  full  acid  color  without  causing  a  secondary  change  of  color  (see  table 

35  for  quantities) The  volume  is  at  once  made  up   in  all 

the  tubes  to  a  constant  height  (within  about  one  drop)  with  distilled  water, 
the  height  corresponding  to  5  cc. 

These  pairs  are  used  in  the  comparator  and  matched  with  the 
tested  solution.  This  tested  solution  is  added  to  ten  drops  of  the 
proper  indicator  until  a  volume  of  5  cc.  is  attained  and  the  tube 
is  then  placed  in  the  comparator  backed  by  a  water  blank. 

Gillespie  describes  the  use  of  the  comparator  (page  70)  and  a 
modification  for  the  accommodation  of  sets  of  three  tubes  used 
when  colored  solutions  have  to  be  compared.  He  also  discusses 
a  number  of  minor  points  and  cautions  against  the  indiscriminate 
comparison  of  measurements  taken  at  different  temperatures. 
For  the  details  the  original  papers  should  be  consulted.  Were 
it  not  that  the  writer  has  seen  evidence  that  the  method  has  been 
applied  with  neglect  of  volume  or  concentration  relations  called 
for  by  the  theory  involved  and  carefully  specified  by  Gillespie, 
it  would  seem  unnecessary  to  advise  that  the  principles  be  under- 
stood before  the  method  is  used.  Certain  other  misconceptions 
of  theory  and  practice  found  in  a  treatment  of  the  method  by 
Medalia  (1920)  have  been  corrected  by  Gillespie  (1921). 

A  very  judicious  appraisal  of  the  method's  value  was  given  by 
Gillespie  in  these  words: 

The  method  should  be  of  especial  use  in  orienting  experiments,  or  in 
occasional  experiments  involving  hydrogen  ion  exponent  measurements, 
either  where  it  is  unnecessary  to  push  to  the  highest  degree  of  precision 
obtainable,  or  where  the  investigator  may  be  content  to  carry  out  his 
measurements  to  his  limit  of  precision  and  to  record  his  results  in  such  a 
form  that  they  may  be  more  closely  interpreted  when  a  more  precise  study 
of  indicators  shall  have  been  completed. 

For  the  elaboration  of  certain  manipulative  details  see  Van 
Alstine  (1920). 

If  an  indicator  has  only  one  color,  for  instance  if  it  is  yellow 
in  the  alkaline  form  and  colorless  in  the  acid  form,  it  is  evident 
that  the  method  employed  by  Gillespie  may  be  used  with  the 
slimination  of  one  of  the  sets  of  tubes.     Thus  if  10  cc.  of  a  tested 


132 


THE   DETERMINATION   OF   HYDROGEN   IONS 


solution  containing  1  cc.  of  para  nitro  phenol  matches  10  cc.  of 
an  alkaline  solution  containing  0.2  cc.  of  the  same  solution  of 
the  same  indicator,  it  is  known  that  the  tested  solution  has  in- 
duced a  20  per  cent  transformation  of  the  indicator.  Then  a 
is  0.2.  If  now  KIA  has  been  determined,  and  if  it  has  been  shown 
that  the  simple  dissociation  formula  holds  for  the  indicator  in 
use,  equation  10  may  be  solved  for  pH. 

This  procedure  has  been  developed  by  Michaelis  and  co- 
workers; Biochem.  Z.  (1920)  109,  165;  Biochem.  Z.  (1921)  119, 
307;  Deut.  med.  Wochenschr.  (1920)  46,  1238;  47,  465,  673; 
Z.  Nahr.  Genussm.  (1921)  42,  75;  Z.  Immunitatsf.  (1921)  32, 
194;  Wochenschrift   Brau.    (1921)    38,    107.      Calculations    are 

ot 

aided  by  the  use  of  a  table   relating  a  to  log  - .     Such    a 

1  — a 

table,  somewhat  more  elaborate  than  that  required  for  this  special 
purpose,  will  be  found  on  page  460  of  the  appendix. 

It  is  obviously  necessary  that  KIA  shall  have  been  determined 
or  that  the  actual  experimental  data  relating  the  degree  of  color 
transformation  to  pH  along  the  "dissociation  curve"  shall  have 
been  obtained.  This  necessary,  fundamental  "calibration" 
has  been  worked  out  by  Michaelis  and  Gyemant  (1920)  and 
Michaelis  and  Kriiger  (1921)  (using  hydrogen  electrode  measure- 
ments as  a  basis)  for  a  series  of  one-color  indicators.  In  the  fol- 
lowing table  are  the  pH  values  of  the  half -transformation  points 
of  the  indicators  used  by  Michaelis  and  Gyemant.     These  points 

correspond  to  log  =r~  (see  p.  26). 

-"■TA 


TABLE  36 
pH  values  of  the  half-transformation  points  of  indicators.    After  Michaelis 


2,  6  dinitro  phenol. . . 
2,  4  dinitro  phenol. . . 

p-nitro  phenol 

m-nitro  phenol 

Phenolphthalein 

Alizarine  Yellow  GG 


TEMPERATURE 

10° 

20° 

30° 

40° 

3.74 

3.68 

3.62 

3.56 

4.11 

4.05 

3.99 

3.93 

7.27 

7.16 

7.04 

6.93 

8.43 

8.32 

8.21 

8.09 

9.82 

9.70 

9.58 

9.46 

11.26 

11.13 

11.00 

10.87 

50° 


3.51 
3.85 
6.81 
7.99 
9.34 
10.74 


APPROXIMATE   INDICATOR  METHODS 


133 


Now  phenolphthalein,  as  we  have  already  mentioned,  is  poly- 
acidic  with  dissociation  constants  so  close  to  one  another  that 
the  simple  equation  of  a  mono  acid  cannot  be  used.  Alizarine 
Yellow  GG  suffers  the  same  disadvantage.  Consequently  it  is 
necessary  in  these  cases  to  abandon  the  simple  equation  and  the 
dissociation  constants  given  above  and  to  tabulate  the  experi- 
mental data.  Michaelis  and  Gyemant  have  given  the  following 
tabulations. 

TABLE  37 
Degree  of  color,  a,  shown  by  phenolphthalein  at  indicated  pH  values. 
Temperature  18°C. 


a 

pH 

a 

pH 

(X 

pH 

0.01 

8.45 

0.16 

9.10 

0.55 

9.80 

0.014 

8.50 

0.21 

9.20 

0.60 

9.90 

0.030 

8.60 

0.27 

9.30 

0.65 

10.00 

0.047 

8.70 

0.34 

9.40 

0.70 

10.10 

0.069 

8.80 

0.40 

9.50 

0.75 

10.20 

0.090 

8.90 

0.45 

9.60 

0.80 

10.30 

0.120 

9.00 

0.50 

9.70 

0.845 
0.873 

10.40 
10.50 

TABLE  38 
Degree  of  color,  a,  shown  by  alizarine  yellow  GG  at  indicated  pH  values. 

Temperature  20°C. 


a 

PH 

a 

pH 

0.13 

10.00 

0.56 

11.20 

0.16 

10.20 

0.66 

11.40 

0.22 

10.40 

0.75 

11.60 

0.29 

10.60 

0.83 

11.80 

0.36 

10.80 

0.88 

12.00 

0.46 

11.00 

For  2,  5-dinitrophenol  log 


K, 


is  5.15  for  solutions  of  very 


low  salt  concentrations,  5.08  for  solutions  of  0.15  M  salt  concen- 
tration and  5.02  for  solutions  of  0.5  M  salt  concentration. 

For  3,  4-dinitro  phenol  log  ~zz~  is  about  5.3  and  for  2,  3-dini- 

-"■IA 

trophenol  about  4.8. 


134  THE   DETERMINATION    OF   HYDROGEN   IONS 

With  these  data  we  are  now  prepared  to  measure  pH  values 
without  the  use  of  standard  buffer  solutions. 
The  following  indicator  solutions  are  used: 

1.  2,  4  dinitro  phenol  (a  dinitro  phenol)  0.05  per  cent  aqueous  solution 

2.  2,  6  dinitro  phenol  (/3  dinitro  phenol)  saturated  aqueous  solution 

formed  at  high  temperature  and  filtered  from  crystals. 

3.  2,  5  dinitro  phenol   (y  dinitro  phenol)  0.025  per  cent-  aqueous 

solution. 

4.  3,  4  dinitro  phenol  (5  dinitro  phenol)  concentration  not  given. 

5.  2,  3  dinitro  phenol  (e  dinitro  phenol)  concentration  not  given. 

6.  p-nitro  phenol  0.1  per  cent  aqueous  solution. 

7.  m-nitro  phenol  0.3  per  cent  aqueous  solution. 

8.  phenol  phthalein  0.04  per  cent  solution  in  30  per  cent  alcohol. 

9.  Alizarine  yellow  GG  (salicyl  yellow,  m-nitrobenzene  azo  salicylic 

acid)  saturated  alcoholic  solution  diluted  to  convenient  strength. 

Test  tubes  must  be  of  equal  bore.  A  measured  amount  of  the 
solution  to  be  tested  (e.g.  10  cc.)  is  mixed  with  the  proper  indicator 
in  such  amount  that  a  rather  weak  color  is  developed.  To  a 
second  test  tube  containing  9  cc.  N/100  NaOH  there  is  added 
such  a  volume  of  the  indicator  solution  that  the  color  developed 
approximately  matches  that  of  the  first  tube.  The  volume  of 
the  second  tube  is  now  made  up  to  the  volume  of  the  first.  If  the 
two  tubes  do  not  match  in  color,  another  trial  is  made  with  more 
or  less  indicator  until  a  color  match  is  obtained.  The  amount 
of  fully  transformed  indicator  in  the  second  tube  then  corresponds 
to  that  amount  of  indicator  in  the  first  tube  which  has  been  trans- 
formed to  the  colored  tautomer.  Let  us  assume  that  1.0  cc. 
was  added  to  the  tested  solution  and  that  a  color  match  occurs 
when  0.1  cc.  of  the  same  indicator  solution  was  placed  in  the  second 
alkaline  tube  and  made  up  to  the  volume  of  the  first.  Then  the 
percentage  color  transformation  induced  by  the  tested  solution 

was  10. 

a 

Hence  a  =  0.1  and  log =   —   0.95. 

1  — a 

If  the  indicator  used  was  p-nitrophenol  and  the  temperature 
was  20°C.     pH  =  7.16  -  .95  =  6.21  (6.2) 

If  the  indicator  was  phenolphthalein  table  37  shows  that  the 
pH  was  about  9.0. 

For  routine  work  in  the  range  pH  2.8  to  8.4  Michaelis  (1921) 
recommends  the  following  system. 


APPROXIMATE   INDICATOR   METHODS 


135 


To  uniform  test  tubes  are  added  seriatim  the  volumes  of  indica- 
tor solution  given  in  the  following  tables,  the  indicator  solution 
being  prepared  by  diluting  the  stock  solutions  (page  134)  ten  times 
with  0.1  normal  soda  solution  (sic).  Each  tube  is  now  filled  to  a 
7  cc.  mark  with  the  soda  (sic)  solution.  (In  the  original  paper 
Michaelis  and  Gyemant  describe  dilutions  with  N/100  NaOH 
solution.) 

TABLE  39 

m-nitro  phenol 


Tube  number 

Cubic  centimeters  of  indicator. 
pH 


1 
5.2 

8.4 


2 

4.2 
8.2 


3 
3.0 

8.0 


4 
2.3 

7.8 


5 
1.5 
7.6 


6 
1.0 
7.4 


7 
0.66 
7.2 


0.43 
7.0 


9 
0.27 
6.8 


p-nitro  phenol 


Tube  number 

Cubic  centimeters  of  indicator. . 
pH 


10 

11 

12 

13 

14 

15 

16 

17 

4.05 

3.0 

2.0 

1.4 

0.94 

0.63 

0.4 

0.25 

7.0 

6.8 

6.6 

6.4 

6.2 

6.0 

5.8 

5.6 

18 
0.16 
5.4 


#,  5-dinitro  phenol  (y  dinitro  phenol) 


Tube  number 

19 
6.6 

5.4 

20 
5.5 
5.2 

21 
4.5 
5.0 

22 
3.4 

4.8 

23 
2.4 
4.6 

24 
1.65 
4.4 

25 
1.1 

4.2 

26 

pH 

0.74 
4  0 

2,  4-dinitro  phenol  (a  dinitro  phenol) 


Tube  number 

Cubic  centimeters  of  indicator. 
pH 


27 

28 

29 

30 

31 

32 

33 

34 

6.7 

5.7 

4.6 

3.4 

2.5 

1.74 

1.20 

0.78 

4.4 

4.2 

4.0 

3.8 

3.6 

3.4 

3.2 

3.0 

35 
0.51 

2.8 


The  test  tubes  are  sealed  with  paraffined  corks  and  when  not 
in  use  are  protected  from  the  light. 

To  test  a  solution  for  its  pH  value  6  cc.  are  taken  and  1  cc. 
indicator  solution  added.  The  solution  is  then  compared  with 
the  standards. 

For  testing  the  pH  values  of  waters  Michaelis  (1921)  operates 
as  follows: 

A  stock  solution  containing  0.3  gram  pure  m-nitro  phenol  in 
300  cc.  distilled  water  is  diluted  before  use  by  adding  to  1  cc. 
of  the  stock  9  cc.  distilled  water.  There  are  used  flat  bottom 
tubes  of  about  25  cm.  height  and  14  mm.  internal  diameter  having 
such  uniformity  that  40  cc.  of  water  will  stand  at  a  height  of 


136  THE    DETERMINATION   OF   HYDROGEN   IONS 

between  22  and  23  cm.  To  six  such  tubes  are  added  seriatim 
0.25;  0.29;  0.33;  0.38;  0.45  and  0.50  cc.  of  the  diluted  m-nitro 
phenol  solution.  To  each  tube  are  added  40  cc.  of  an  approximately 
N/50  NaOH  solution  freshly  prepared  by  dilution  of  an  approxi- 
mately normal  solution.    These  are  the  standards. 

To  test  a  water,  40  cc.  are  added  to  a  tube  of  correct  dimensions 
and  to  this  is  added  sufficient  indicator  to  develop  a.  color  within 
the  range  of  the  standards,  preferably  near  the  brighter  of  the 
standards.  Comparison  is  now  made  as  in  Nesslerization,  after 
having  waited  two  minutes  for  completion  of  the  mixing. 

The  amount  of  indicator  in  the  alkaline,  matching  standard 
corresponds  to  the  amount  transformed  to  the  colored  form  by 
the  tested  solution.  Therefore,  the  cubic  centimeters  of  indica- 
tor in  the  standard  divided  by  the  cubic  centimeters  in  the  tested 
solution  is  a,  the  degree  of  color  transformation,  or  when  multi- 
plied by  100  the  percentage  color  transformation. 

Michaelis  and  his  co-workers  have  tabulated  corrections  for 
temperature  and  for  salt  concentrations.  The  operator  should 
determine  for  himself  not  only  the  order  of  accuracy  required  in 
his  problem  but  his  own  ability  to  make  readings  with  that  pre- 
cision which  will  make  corrections  significant.  He  may  then 
refer  to  the  original  papers  for  tables  giving  corrections  for  salt 
effects  and  for  temperature.  The  order  of  magnitude  of  these 
corrections  may  be  seen  in  the  following  example. 

For  m-nitrophenol  Michaelis  and  Kriiger  give  the  following 

values  of  log  zz~  at  17°C.  in  solutions  of  the  indicated  salt 
concentrations. 

TABLE  40 


MOLECULAR  8ALT  CONTENT 

KAI 

O-0.01 

8.33 

0.05 

8.28 

0.10          i 

8.23 

0.15 

8.22 

0.20 

8.18 

0.3-0.6 

8.17 

to  1.0 

8.15 

APPROXIMATE    INDICATOR    METHODS 


137 


The  temperature  corrections  to  be  added  when  m-nitrophenol 
is  used  at  temperatures  other  than  17.5°C.  are  as  follows. 


TABLE  41 


t° 

CORRECTION 

t° 

CORRECTION 

5 

+0.10 

25 

-0.06 

10 

+0.06 

30 

-0.11 

15 

+0.02 

35 

-0.15 

17.5 

±0.00 

40 

-0.18 

20 

-0.02 

45 

-0.22 

50 

-0.26 

In  spite  of  the  fact  that  the  nitro  compounds  used  by  Micha- 
elis  and  Gyemant  are  of  wan  color  and  those  tried  in  the  survey 
made  by  Clark  and  Lubs  were  neglected  for  this  reason,  Micha- 
elis  and  Gyemant  describe  the  application  of  their  method  to 
colored  solutions. 

Advantage  is  taken  of  the  fact  that  many  solutions  are  inappre- 
ciably altered  in  pH  by  diluting  five  or  even  ten  times  (see  page 
37).  For  dilution,  Michaelis  and  Gyemant  use  freshly  boiled 
NaCl  solution  of  a  concentration  approximately  that  of  the  test 
solution.  If  on  dilution  the  natural  color  still  interferes  with 
the  use  of  an  indicator,  the  natural  color  may  be  duplicated  in 
the  standard  by  the  use  of  supplementary  dyes  such  as  S0rensen 
uses.  Or,  if  addition  of  alkali  does  not  alter  the  natural  color  of 
the  solution  under  test,  the,  standard  may  be  made  up  with  an 
alkaline  solution  of  the  tested  solution  itself.  In  this  case  it  is 
necessary  to  be  on  guard  against  the  buffer  action  and  to  add 
alkali  until  no  increase  in  the  color  of  the  indicator  is  observed. 

Without  doubt  the  preferable  procedure  to  follow  when  apply- 
ing the  Michaelis  and  Gyemant  method  or  any  other  method  to 
colored  solutions  is  to  use  the  "comparator"  described  on  page 
70  and  illustrated  in  figure  8. 

The  method  of  Michaelis  and  Gyemant  is  fundamentally  the 
same  as  that  of  Gillespie  and  should,  therefore,  be  used  with  the 
qualifications  which  Gillespie  has  stated.  There  is  a  distinct 
advantage  in  the  use  of  the  nitro  phenols  for  they  have  been  found 
to  have  relatively  small  protein  and  salt  errors.  It  is  sometimes 
accessary  to  use  very  high  concentrations  of  the  indicator,  and 


138  THE   DETERMINATION   OF   HYDROGEN   IONS 

in  such  circumstances  one  must  be  on  guard  against  the  effect  of 
the  indicator  itself  or  of  impurities. 

Indicator  paper.  Although  a  favorite  form  of  indicator  is  the 
deposit  on  a  strip  of  paper  (for  example  the  familiar  litmus  paper) 
it  is  to  be  avoided  unless  the  use  of  an  indicator  solution  is  pre- 
cluded. It  is  to  be  avoided  because  the  factors  involved  in  the 
reaction  between  solution  and  indicator  are  made  complex  by 
the  capillary  action  of  the  paper  or  the  material  entrained  in 
these  capillaries.  On  the  other  hand  there  are  occasions  when 
an  approximate  measure  of  pH  is  sufficient  and  when  an  indicator- 
paper  is  to  be  preferred.  On  such  an  occasion  it  is  desirable  to 
know  the  difficulties  to  be  encountered.  We  are  indebted  to 
Walpole  (1913)  and  others  but  particularly  to  Kolthoff  (1919, 
1921)  for  investigations  on  this  subject.  Kolthoff  has  given 
particular  attention  to  the  sensitivity  of  indicator  papers  when 
used  in  titrations,  a  situation  where  there  is  generally  but  little 
buffer  action  near  the  end-point.  Under  such  circumstances 
there  are  to  be  regarded  a  number  of  details  which  are  described 
at  length  in  Kolthoff' s  papers.  Several  of  these  details  will  be 
perceived  if  we  describe  some  of  the  more  important  aspects  of 
the  indicator-paper  method  of  determining  pH. 

In  general  one  must  ride  either  horn  of  the  following  dilemma. 
The  paper  is  sized,  in  which  case  the  buffer  action  of  the  tested 
solution  must  be  strong  enough  and  allowed  time  enough  to  over- 
come the  buffer  action  of  the  sizing.  Or  the  paper  has  the  quali- 
ties of  filter  paper,  in  which  case  the  solution  tested  will  spread 
and  leave  rings  of  different  composition  formed  by  the  adsorp- 
tive  power  of  the  capillaries. 

Kolthoff  found  that  various  treatments  and  selections  of  filter 
paper  are  of  secondary  importance,  so  the  choice  lies  between 
sized  and  unsized  paper.  Now  certain  coloring  matters  are  ad- 
sorbed by  filter  paper  so  that  a  separation  is  possible  and  the 
clear  solution  can  be  found  in  a  ring  about  the  point  of  contact 
between  a  tested  colored  solution  and  the  indicator  paper.  But 
beyond  this  ring  is  a  much  more  dilute  one  and  unless  one  knows 
the  properties  of  the  system  under  examination  it  is  not  easy  to 
correctly  estimate  the  pH  of  the  solution  from  the  appearances 
of  the  paper. 

Although  coated  paper  may  lose  in  sensitivity  by  not  taking 


APPROXIMATE    INDICATOR   METHODS  139 

up  so  much  indicator  as  filter  paper  and  must  be  used  with  strongly 
buffered  solutions  it  is  the  more  convenient.  In  any  case  the 
paper  should  be  left  in  contact  with  the  tested  solution  a  generous 
length  of  time,  for  the  establishment  of  equilibrium  may  be  very 
slow  (Walpole),  and  there  must  be  instinctively  exercised  a  men- 
tal plotting  of  the  time  curve. 

If,  after  having  exhausted  all  other  methods,  it  is  found  that 
the  indicator-paper  method  is  the  better  adapted  to  a  particular 
set  of  circumstances,  the  procedure  should  be  calibrated  to  the 
purpose  at  hand  rather  than  forced  to  render  accurate  pH  values. 

Dilution.  As  indicated  in  Chapter  II  a  well  buffered  solution 
may  often  be  moderately  diluted  without  seriously  altering  the 
pH. 

When  dealing  with  complex  solutions  which  are  mixtures  of 
very  weakly  dissociated  acids  and  bases  in  the  presence  of  their 
salts,  and  especially  when  the  solution  is  already  near  neutrality 
dilution  has  a  very  small  effect  on  pH,  so  that  if  we  are  using  the 
crude  colorimetric  method  of  determining  pH  a  five-fold  dilution 
of  the  solution  to  be  tested  will  not  affect  the  result  through  the 
small  change  in  the  actual  hydrogen  ion  concentration.  Differ- 
ences which  may  be  observed  are  quite  likely  to  be  due  to  change 
in  the  protein  or  salt  content.  For  this  reason  as  well  as  for  other 
reasons  Glark  and  Lubs  (1917)  considered  it  wise  to  use  M/20 
standard  comparison  solutions  instead  of  more  concentrated  stand- 
ards for  bacteriological  media  where  dilution  is  often  advantageous. 
The  salt  content  of  the  standards  undoubtedly  influences  the 
indicators  and  should  be  made  as  comparable  as  is  convenient 
with  the  salt  content  of  the  solutions  tested  when  these  are  diluted 
to  obtain  a  better  view  of  the  indicator  color. 

The  conclusion  that  dilution  has  little  effect  on  the  hydrogen 
ion  concentrations  of  many  solutions  has  long  been  recognized. 
Michaelis  (1914)  found  little  change  in  the  pH  of  blood  upon 
dilution,  and  Levy,  Rowntree,  and  Marriott  (1915)  depended 
upon  this  in  part  in  their  dialysis  method  for  the  colorimetric 
determination  of  the  hydrogen  ion  concentration  of  blood.  Hen- 
derson and  Palmer  (1913)  have  used  the  dilution  method  in  de- 
termining the  pH  of  urines,  and  Paul  (1914)  records  some  experi- 
ments with  wines  the  pH  values  of  which  were  affected  but  little 
by  dilution.     The  legitimacy  of  dilution  has  been  tacitly  admitted 


140  THE   DETERMINATION   OF   HYDROGEN   IONS 

by  bacteriologists  in  their  procedure  of  diluting  media  to  be 
titrated  to  what  is  in  reality  a  given  pH  as  indicated  by 
phenolphthalein. 

In  the  examination  of  soil  extracts  colorimetrically  little  could 
be  done  were  the  "soil-solution"  not  diluted.  Whatever  may  be 
the  effect  it  is  certain  that  the  correlations  between  the  pH  values 
of  such  extracts  and  soil  conditions  is  proving  of  great  value  (see 
Chapter  XXI).  Wherry  has  developed  a  field  kit  of  the  sulfon 
phthalein  indicators  with  which  he  has  found  some  remarkable 
correlations  between  plant  distribution  and  the  pH  of  the  native 
soils.     This  field  kit  is  now  on  the  market. 

The  use  of  indicators  in  bacteriology.  Perhaps  no  other  science 
requires  such  continuous  routine  use  of  indicators  as  does  bac- 
teriology. This  use  is  chiefly  in  the  adjustment  of  the  reaction 
of  culture  media  and  in  the  testing  of  the  direction  and  limits  of 
fermentation.  While  these  are  but  examples,  the  frequency  with 
which  they  become  matters  of  routine  warrant  a  brief  outline  of 
special  procedures. 

If  experience  has  shown  that  the  pH  of  the  medium  may  lie 
within  a  zone  about  0.5  units  of  pH  wide,  it  is  sufficient  to  add 
unstandardized  acid  or  alkali,  as  the  case  may  be,  until  a  portion 
of  the  medium  tested  with  the  proper  indicator  in  proper  concen- 
tration approximately  matches  that  color  standard  shown  in  the 
color  chart  of  page  50  corresponding  to  the  pH  value  to  be  ap- 
proximated. This  requires  experience  in  overcoming  the  confusing 
effect  of  the  natural  color  of  the  medium  and  also  a  well  established 
sense  of  color  memory.  The  beginner  should  proceed  in  some 
such  way  as  the  following. 

It  is  desired,  for  instance,  to  adjust  a  colorless  medium  to  pH 
7.5.  The  medium  as  prepared  is  somewhat  below  the  final  vol- 
ume. A  quick,  rough  test  at  room  temperature  shows  that  the 
pH  value  lies  between  6.0  and  6.5.  Therefore,  alkali  must  be 
added.  The  'alkali  solution  to  be  used  need  not  be  standardized 
but  may  be  about  1  normal.  An  exact  one-in-ten  dilution  of 
this  is  run  into  5  cc.  of  the  medium  to  which  has  been  added  5 
drops  of  phenol  red  solution.  Titration  is  continued  until  the 
color  nearly  matches  10  cc.  of  standard  buffer  "7.5."  The  tube 
of  medium  is  now  diluted  to  10  cc.  so  that  a  color  comparison 
may  be  made  between  test  solution  and  standard,  each  contain- 


APPROXIMATE   INDICATOR   METHODS  141 

s 

ing  the  same  concentration  of  indicator.  The  tubes  are  viewed 
through  equal  depths  of  solution.  If  the  desired  point  7.5  has 
been  overstepped  another  trial  is  made.  If  7.5  is  not  reached  a 
moderate  addition  of  alkali  may  be  made  without  serious  viola- 
tion of  volume  requirements,  and  a  second  reading  is  taken. 

Having  made  estimates  of  the  pH  values  in  the  two  readings 
an  interpolation  is  made  of  the  amount  of  dilute  alkali  required 
to  bring  the  medium  to  exactly  pH  7.5.  From  this  is  calculated 
the  amount  of  the  stronger  alkali  required  for  the  main  batch. 
Having  added  this  a  check  determination  is  made.  When 
finally  adjusted  the  medium  is  diluted  to  its  final  volume.  Most 
culture  media  suffer  alterations  of  their  pH  values  during  sterili- 
zation and  consequently  allowance  must  be  made  if  the  final 
pH  value  is  to  be  exact.  This  allowance  will  vary  with  the  medium 
but  can  easily  be  determined  for  a  standard  medium  prepared 
under  uniform  conditions. 

When  the  color  or  turbidity  of  a  tested  solution  interferes  with 
direct  color  comparisons  proceed  as  above  but  make  comparisons 
by  means  of  the  Walpole  compensation  method  described  on 
page  70. 

It  need  hardly  be  said  that  if  the  requirements  of  an  organism 
are  such  that  the  desired  pH  value  cannot  be  obtained  with  phenol 
red  a  more  suitable  indicator  is  selected  from  table  6  and  if  the 
medium  requires  the  addition  of  acid  an  unstandardized  acid 
solution  approximately  normal  (or  stronger)  and  an  exact  1:10 
dilution  of  this  are  substituted  for  the  alkali  solutions  mentioned 
above. 

In  testing  fermentations  it  often  happens  that  the  final  hydro*- 
gen  ion  concentration  is  of  more  significance  than  the  amount  of 
acid  or  alkali  formed;  but  the  two  distinct  types  of  data  are  not 
to  be  confused  to  the  complete  displacement  of  either.  It  is 
sometimes  convenient  to  incorporate  the  indicator  with  the 
medium  provided  the  indicator  is  not  reduced  or  destroyed  by 
the  bacterial  action.  The  sulfon  phthaleins  are  particularly  use- 
ful for  they  are  not  reduced  except  by  the  more  active  anaerobes. 
Brom  cresol  purple  replaces  litmus  in  the  common  milk-fermenta- 
tion tests  without  introducing  that  confusion  which  the  reduction 
of  litmus  causes.  It  reveals  differences  in  pH  even  beyond  the 
range  of  its  usefulness  for  ordinary  measurements,  passing  from  a 


142  THE   DETERMINATION   OF   HYDROGEN   IONS 

greyish  blue  in  normal  milk  to  more  and  more  brilliant  yellows 
with  the  development  of  acidity,  and  to  a  deep  blue  with  the 
development  of  alkalinity.  For  further  details  see  Clark  and 
Lubs  (1917). 

In  the  method  of  Clark  and  Lubs  (1915,  1916)  for  the  differenti- 
ation of  the  two  main  groups  of  the  coli-aerogenes  bacteria,  as 
well  as  in  the  similar  method  of  Avery  and  Cullen  (1919)  for 
separating  streptococci,  the  composition  of  the  medium  is  so 
adjusted  to  the  metabolic  powers  of  the  organisms,  that  the 
reaction  is  left  acid  to  methyl  red  in  one  case,  and  alkaline  in 
the  other.  No  exact  pH  measurements  are  necessary.  In  cases 
where  large  numbers  of  cultures  falling  within  the  range  of  one 
indicator  are  to  be  tested,  the  cultures  may  be  treated  with  the 
indicator  and  compared  by  grouping.  A  careful  determination 
made  upon  one  member  of  a  homogeneous  group  will  serve  for  all. 
In  this  way  large  numbers  of  cultures  may  be  tested  in  a  day. 

Special  uses.  While  on  the  subject  of  approximate  determina- 
tions with  indicators  a  word  may  be  said  about  the  usefulness  of 
the  quick,  rough  test. 

Almost  every  investigator  has  come  to  realize  that  among  the 
mistakes  in  labeling  chemicals  the  more  frequent  are  cases  in 
which  a  basic  salt  is  labeled  as  an  acid  salt  and  vice  versa.  Now 
a  solution  of  NajjHPC^,  for  example,  has  a  pH  value,  which, 
while  easily  displaced  (see  figure  5),  distinguishes  it  definitely 
from  a  solution  of  NaH2P04  or  Na3P04.  Indeed  some  idea  may 
be  obtained  of  the  degree  of  impurity  if  the  pH  value  of  a  dilute 
solution  is  displaced  definitely  from  about  pH  8.5.  Some  serious 
accidents  are  said  to  have  occurred  in  medical  practice  by  the 
use  of  sodium  citrate  purported  to  be  neutral  and  too  late  found 
to  be  acidic.  One  short,  swift  test  with  an  indicator  could  have 
revealed  the  situation,  and  averted  the  accident. 

Indeed  there  are  a  great  many  substances  solutions  of  which 
have  either  a  buffered  and  definite  pH  value,  as  in  the  case  of 
acid  potassium  phthalate,  or  else  a  pH  value  easily  displaced 
by  impurities  from  that  of  the  absolutely  pure  substance  but 
still  falling  within  limits,  as  in  the  case  of  the  primary  and  second- 
ary phosphates.  When  properly  defined,  such  values  can  be 
made  part  of  the  specifications  for  purity.  Especially  in  the 
case  of  drugs  which  are  often  used  beyond  the  reach  of  the  assay 


APPROXIMATE    INDICATOR   METHODS  143 

laboratory  a  simple  indicator  test  should  prove  helpful  as  sug- 
gested by  Evers  (1921)  and  especially  emphasized  by  Kolthoff 
(1921). 

In  the  case  of  milk  it  is  quite  impossible  to  define  the  pH  by  a 
comparison  of  the  color  of  an  indicator  in  the  milk  with  the 
color  of  the  indicator  in  a  clear  standard;  yet  differences  are  made 
distinctly  evident,  and,  if  taken  only  for  what  they  actually 
mean,  are  helpful  in  the  grading  of  milk  and  in  the  study  of  the 
conduct  of  different  bacteria  inoculated  into  sterile  milk.  Clark 
and  Lubs  (1917)  called  attention  to  the  superiority  of  the  sul- 
fonphthalein  indicators,  especially  brom  cresol  purple,  for  this 
purpose. 

Spotting.  When  only  small  quantities  of  solution  are  available  or 
when  highly  colored  solutions  are  to  be  roughly  measured,  their  ex- 
amination in  drops  against  a  brilliant  white  background  of  "opal" 
glass  is  often  helpful.  In  the  examination  of  colorless  solutions 
comparisons  with  standards  may  be  made  as  follows.  A  drop  of 
the  solution  under  examination  is  mixed  with  a  drop  of  the  proper 
indicator  solution  upon  a  piece  of  opal  glass.  About  this  are 
placed  drops  of  standard  solutions  and  with  each  is  mixed  a 
drop  of  the  indicator  solution  used  with  the  solution  under 
examination.  Direct  comparison  is  then  made.  Felton  who 
developed  details  in  this  method  for  the  examination  of  small 
quantities  of  solutions  used  in  tissue-culture  investigations  found 
mixtures  of  indicators  of  particular  value  for  orientation.  Equal 
parts  of  methyl  red  and  brom  thymol  blue,  for  instance,  give 
brilliant  color  contrasts  in  this  drop  method  between  about  pH 
4.6  and  7.6;  but  with  an  unsatisfactory  zone  between  5.6  and  6.2. 
Methyl  red  and  brom  cresol  purple  are  used  between  pH  4.6 
and  7  while  for  rough  work  between  1.2  and  9  methyl  red  and 
thymol  blue  are  used.  These  mixtures  are  used  only  as  "feel- 
ers." The  opal  glass  or  porcelain  upon  which  the  tests  are  to  be 
made  should  be  carefully  tested  for  the  absence  of  material 
seriously  affecting  the  acid-base  equilibria  of  the  material  under 
examination.  Errors  due  to  unequal  drops,  evaporation  and 
impurity  of  indicator  are  to  be  watched  for.  For  further  details 
see  Felton  (1921). 


CHAPTER  IX 

Outline  of  the  Electrometric  Method 

A  noble  metal  coated  with  platinum  black,  which  will  hold  large 
quantities  of  hydrogen,  may  be  made  to  serve  as  a  hydrogen  elec- 
trode. When  it  is  laden  with  hydrogen  and  immersed  in  a  solution 
containing  hydrogen  ions,  there  is  exhibited  a  difference  of  elec- 
trical potential  between  solution  and  electrode  which  is  depend- 
ent upon  the  concentration  of  the  hydrogen  ions;  just  as  the 
potential  difference  between  a  silver  electrode  and  a  solution  of 
silver  ions  is  dependent  upon  the  concentration  of  the  silver  ions. 

We  have  no  reliable  means  of  measuring  this  single  potential 
difference;  but  when  we  join  two  hydrogen  electrodes,  as  shown 
in  figure  13,  we  can  not  only  measure  the  difference  between  the 
aforementioned  differences  of  potential,  i.e.,  the  total  electro- 
motive force  (E.  M.  F.)  of  the  "gas  chain"  as  it  is  called,  but  we 
can  also  derive  an  equation  showing  how  this  E.  M.  F.  will  vary 
with  the  ratio  of  the  concentrations  of  the  hydrogen  ions  about 
the  two  electrodes.  If  C  is  the  concentration  of  the  hydrogen  ions 
in  one  solution  and  C  the  concentration  in  the  other,  the  E.  M.  F. 
of  the  combination  will  be  related  to  the  ratio  of  the  concentrations 
by  the  following  equation  expressed  in  numerical  form  for  a 
temperature  of  25°C. 

E.  M.  F.  =  0.059  log  §- 
C 

We  shall  leave  to  the  next  chapter  the  derivation  of  the  equa- 
tion and  shall  now  put  it  in  a  form  not  restricted  to  the  particular 
temperature  of  25°C.  assumed  above. 

C 
E.  M.  F.  =  0.000,198,37  T  log  ~; 

Here  T  is  the  absolute  temperature,  the  zero  point  of  which  is 
273.09°  below  0°C.  A  table  giving  the  values  of  0.000,198,37  T 
for  various  temperatures  centigrade  is  given  in  the  Appendix. 
Thus  if  we  join  two  hydrogen  electrodes  as  illustrated  in  figure 
13  measurements  of  the  electromotive  force  of  the  chain  and  of 

144 


OUTLINE    OF   ELECTROMETRIC   METHOD 


145 


the  temperature  allow  us  to  calculate  the  ratio  of  the  one  hydro- 
gen ion  concentration  to  the  other.  Then  if  one  hydrogen  ion 
concentration  is  known  we  may  derive  the  other. 

As  the  "known"  there  may  be  used  any  one  of  the  buffer  solu- 
tions described  in  Chapter  VI.  The  reader  should  note,  however, 
that  the  values  of  these   "known"   solutions  are  derived  from 


H, 


i 


[1 


no 


n 


I 


e:->-3£ 


-  -  -  -o- 


I 

n't".'.  * 

SSL, 


ihsos 


=  -=ur=^o^ 


Fig.  13.  Diagram  op  Concentration  Chain  of  Hydrogen  Electrodes 

hydrogen  electrode  measurements  which,  as  we  have  just  seen, 
furnish  ratios  only.  Some  ultimate  standard  is  therefore  implied. 
This  is  discussed  in  Chapter  XIX. 

If  there  be  no  means  at  hand  for  measuring  the  electromotive 
force  but  there  is  available  a  galvanometer  or  a  home-made  capil- 
lary electrometer  for  detecting  small  currents,  the  following 
procedure  may  be  used.  Two  hydrogen  electrodes  are  set  up  as 
in  figure  13.  By  means  of  the  buffer  solutions  described  in  Chap- 
ter VI  the  hydrogen  ion  concentration  in  one  electrode  vessel  is 
varied  until  no  difference  of  potential  occurs  between  the  two 
electrodes.     This  point  is  determined  by  absence  of  deflection 


i 


146  THE   DETERMINATION   OF   HYDROGEN   IONS 

in  the  galvanometer  or  by  no  change  in  the  meniscus  of  the  capil- 
lary electrometer.     Then  C  =  C  in  the  above  equation. 

Instead  of  setting  up  two  hydrogen  electrodes,  one  of  which 
is  a  known  standard,  it  is  generally  more  convenient  to  replace 
the  standard  hydrogen  electrode  by  a  more  permanent  "half 
cell"  such  as  the  "calomel  electrode."  This  is  an  electrode  of 
mercury  covered  with  calomel  in  the  presence  of  a  definite  KC1 
solution,  for  example  saturated  KC1  solution.  If  this  so-called 
"saturated  calomel  electrode"  is  used,  a  tube  containing  sat- 
urated KC1  is  led  directly  to  the  solution  in  the  hydrogen  electrode 
vessel. 

Now  suppose  that  in  the  first  place  there  were  used  two  hydro- 
gen electrodes  as  in  figure  13,  and  let  it  be  assumed  that  one  of 
these  was  immersed  in  a  solution  normal  with  respect  to  hydro- 
gen ions.     Let  C  be  identified  as  1  normal  and  C,  the  unknown 

1 
be  less  than  1  normal.     Then  E.  M.  F.  =  0.000,198,37  T  log  7J 

Now  suppose  that  the  normal  hydrogen  electrode  is  connected 
with  a  "saturated  calomel  electrode."  We  might  then  have 
an  arrangement  as  follows: 

(saturated  calomel  electrode 


II 
III 


►normal  hydrogen  electrode 
(hydrogen  electrode  in  [H+]  =  C' 


I 


Suppose  the  difference  II  has  already  been  determined  and 
that  I  is  measured  in  the  immediate  experiment.  Then  I  — 
II  =  III.  Having  found  III,  we  can  use  the  equation  for  two 
hydrogen  electrodes,  one  of  which  is  the  "normal,"  and  so  solve 
directly  for  C 

At  25°C.  the  mercury  of  the  calomel  electrode  is  0.246  volt 
more  positive  than  the  platinum  of  the  normal  hydrogen  elec- 
trode. 

Hence:  observed  E.  M.  F.  -  0.246  =  III 

I   -   II   =    III 

III  =  0.000,198,37  T  log  pp. 

At  25°C,  T  =  273.09  +  25  =  298.09. 


OUTLINE    OF   ELECTROMETRIC   METHOD  147 

Then  observed  E.  M.  F.  -  0.246  =  0.0591  log  —,. 

But  log  — ;  =  pH. 

Observed  E.M.F.  -  0.246        „ 

=  pH. 

0.0591  F 

If  the  observed  E.  M.  F.  is  0.648,  pH  =  6.80. 

Although  it  is  impracticable  to  describe  at  this  point  the  details 
of  a  complete  system  for  the  measurement  of  hydrogen  ion  con- 
centration an  outline  may  be  given  with  which  to  coordinate 
the  main  features  as  they  will  develop  in  subsequent  chapters. 

Figure  14  illustrates  a  simple  system  which  may  be  put  together 
from  inexpensive  material.  It  is  not  a  system  which  can  be 
recommended  for  precise  or  even  routine  measurements,  but  it 
will  work  and  is  well  adapted  to  show  the  principles  concerned. 

Hydrogen,  prepared  by  one  of  the  methods  described  in  Chap- 
ter XV,  passes  into  the  hydrogen  electrode  vessel  A  and  escapes  • 
at  B.  Connected  with  this  vessel  by  the  siphon  S,  filled  with  a 
saturated  KC1  solution,  is  the  calomel  electrode  M  consisting  of  a 
layer  of  mercury  covered  by  calomel  under  a  saturated  solution 
of  KC1.  The  hydrogen  electrode  H  consists  of  a  piece  of  plati- 
num foil  covered  with  platinum  black.  It  is  welded  to  a  plati- 
num wire  which  is  sealed  into  the  glass  tube. 

Hydrogen  is  bubbled  through  the  solution  in  A  until  solution 
and  electrode  are  thoroughly  saturated  with  the  gas. 

The  difference  between  the  potential  difference  at  the  mercury- 
calomel  junction  and  the  potential  difference  at  the  hydrogen 
3lectrode-solution  junction  is  now  measured  by  means  of  a  po- 
tentiometer.    A  simple  form  of  this  is  illustrated. 

A  storage  battery  P  sends  current  through  the  rheostat  R,  the 
calibrated  resistance-wire  K-L  and  the  fixed  resistance  L-F.  By 
properly  setting  the  switch  O  a  Weston  cell  W  having  an  electro- 
notive  force  of  1.018  volts  can  be  connected  to  K  and  F,  the 
f  pole  of  the  Weston  cell  being  connected  to  the  +  side  of  the 
>attery  current.  The  rheostat  R  is  now  varied  until  there  is 
io  deflection  of  the  galvanometer  or  electrometer  E.  Then  the 
i  lifference  of  potential  between  K  and  F  is  equal  to  the  E.  M.  F. 
t  f  the  Weston  cell.    The  resistance  K-L  is  such  that  when  the 


148  THE   DETERMINATION    OF   HYDROGEN   IONS 

above  adjustment  is  made  the  difference  of  potential  between 
K  and  L  is  one  volt.  A  scale  properly  divided  is  placed  beside 
the  wire  K-L.  When  the  sliding  contact  X  is  at  K  there  will  be 
no  difference  of  potential  between  X  and  K.  When  X  is  at  L 
the  difference  of  potential  between  X  and  K  will  be  one  volt. 
When  X  is  at  some  intermediate  position  the  difference  of  potential 
between  X  and  K  will  be  that  fraction  of  one  volt  indicated  by 
the  scale. 

Having  first  carefully  adjusted  the  potentiometer  by  means 
of  the  standard  Weston  cell  the  switch  O  is  thrown  to  connect 
the  calomel  electrode-hydrogen  electrode  system  and  X  is  slid 
in  one  direction  or  the  other  until  the  galvanometer  E  shows  no 
deflection.  Then  the  difference  of  potential  between  X  and 
K  is  equal  to  the  difference  of  potential  between  mercury  and 
platinum. 

The  temperature  is  read  and  the  data  put  into  the  equations 
given  above. 

Neither  measured  E.  M.  F.  nor  Weston  cell  should  be  left  in 
circuit  for  more  than  an  instant.  While  switch  0  can  be  used 
for  this  momentary  completion  of  circuit,  it  is  more  convenient 
to  use  a  telegraph  key  in  the  galvanometer  circuit. 

If  care  be  taken  to  maintain  the  hydrogen  at  barometric  pres- 
sure, the  effects  of  minor  variations  of  the  barometer  from  sea 
level  conditions  and  of  displacement  of  hydrogen  by  water  vapor 
may  be  neglected  in  rough  measurements.  A  discussion  of  the 
barometric  pressure  is  found  in  the  next  chapter. 

In  all  cases  where  two  unlike  solutions  are  joined  as  in  figure 
13,  there  will  develop  a  local  potential  difference  at  the  liquid 
junction.  To  deal  with  this  precisely  is  the  most  difficult  of  the 
problems  encountered.  The  subject  is  discussed  in  Chapter  XI. 
In  very  many  instances,  however,  the  employment  of  a  saturated 
solution  of  KC1  as  is  specified  in  the  apparatus  illustrated  in 
figure  14,  reduces  the  liquid  junction  potential  difference  to  an 
order  of  magnitude  which  is  negligible. 

Since  variations  may  occur  in  the  calomel  electrode  or  in  the 
reliability  of  the  hydrogen  electrode  it  is  well  to  check  the  system 
frequently  by  means  of  measurements  made  with  standard  solu- 
tions.    Some  of  these  are  described  in  Chapter  XVIII. 

In  the  use  of  the  potentiometer  the  elementary  principles 
must  be  understood  lest  standard  cells  or  half-cells  be  injured 


OUTLINE   OF   ELECTROMETRIC   METHOD 


149 


or  quite  erroneous  results  obtained.     Therefore,  these  principles 
are  discussed  in  Chapter  XIV. 


Fig.  14.  A  Simple  Arrangement  for  Electrometric  Measurement 

of  pH. 

Were  it  not  for  the  fact  that  several  experimenters  have  tried 
to  make  hydrogen  electrode  measurements  by  use  of  conductivity 
nstruments,  it  would  seem  hardly  necessary  to  say  that  the  meas- 
lrement  of  conductivity  or  its  reciprocal,  resistance,  is  a  proce- 
lure  entirely  different  from  the  measurement  of  electromotive 
orces  or  potential  differences.1 

1  The  surprising  number  of  cases  in  which  this  confusion  has  been 
evealed  may  be  an  interesting  psychological  result  of  the  emphasis  hitherto 
)laced  upon  conductivity  measurements,  sometimes  to  the  entire  exclusion 
if  any  reference  to  potentiometric  measurements. 


150  THE   DETERMINATION    OF   HYDROGEN    IONS 

If  the  beginner  is  puzzled  by  the  array  of  apparatus  described 
in  the  following  pages  he  may  welcome  the  following  suggestion. 
The  main  outline  of  a  problem  can  often  be  denned  by  the  use 
of  the  Hildebrand  electrode  used  in  connection  with  the  saturated 
calomel  half-cell  and  by  using  as  a  potentiometer  the  voltmeter 
system.  This  set  of  apparatus  is  illustrated  in  figure  28.  It  not 
infrequently  happens  that  the  outlining  of  a  problem  with  this  or 
a  comparable  system  will  indicate  that  further  refinement  would 
be  useless  or  confusing.  It  also  frequently  happens  that  the  errors 
suggest  phantom  relations  or  obscure  existing  relations  of  im- 
portance. It  is,  therefore,  advisable  whenever  possible  to  keep 
the  accuracy  of  measurements  just  ahead  of  the  immediate  de- 
mands. To  meet  this  requirement  the  investigator  must  gain 
the  ability  to  judge  for  himself  the  apparatus  required  and  it  is 
to  contribute  toward  this  and  the  pleasure  of  work  that  the  follow- 
ing chapters  are  written  in  some  detail.  If  the  reader  does  not 
care  to  work  out  the  peculiar  requirements  of  his  problem  he  is 
advised,  after  having  outlined  his  problem  with  the  system  men- 
tioned above,  to  obtain  a  reliable  potentiometer  of  standard, 
not  unique,  design  and  to  use  the  system  illustrated  in  figure  19. 
In  the  first  instance  accurate  temperature  control  is  unnecessary. 
In  the  second  instance  it  is  advisable  if  for  no  other  purpose  than 
the  avoidance  of  vexatious  uncertainties. 


CHAPTER  X 

Theory  of  the  Hydrogen  Electrode 

In  treating  the  theory  of  the  hydrogen  electrode  we  shall  first 
consider  Nernst's  (1889)  conception  of  electrolytic  solution  tension 
as  a  useful  way  of  remembering  certain  important  relations  and 
then  pass  to  the  thermodynamic  derivation  of  the  E.  M.  F.  of 
a  concentration  cell. 

If  a  metal  be  placed  in  a  solution  of  its  salt  there  will  be  a  differ- 
ence of  electrical  potential  between  metal  and  solution  which  will 
vary  in  an  orderly  manner  with  the  concentration  of  the  metal  ions. 
To  account  for  the  difference  of  potential  Nernst  assumed  that  a 
metal  possesses  a  characteristic  solution  tension  comparable  with 
the  vapor  pressure  of  a  liquid,  or,  better,  with  the  solution  pres- 
sure of  a  crystal  of  sugar — but  with  the  important  qualification 
that  it  is  the  metal  ions  which  pass  into  solution.  Imagine  first 
that  the  metal  is  in  contact  with  pure  water.  The  metal  ions 
passing  into  solution  carry  their  positive  charges  and  leave  the 
metal  negative.  Thus  there  is  established  a  so-called  double 
layer  of  electrical  charges  at  the  interface  between  metal  and  solu- 
tion, the  solution  being  positively  and  the  metal  negatively 
charged  relative  to  one  another.  This  potential  difference  forcibly 
opposes  further  dissolution  of  metallic  ions,  for  the  relative  posi- 
tive electrical  field  in  the  solution  and  the  relative  negative  field 
in  the  metal  restrain  any  further  migration  of  positively  charged 
Dodies  from  the  metal  to  the  solution.  Equilibrium  is  established 
vhen  the  electrostatic  control  equalizes  the  solution  pressure. 
If  now  there  are  already  in  the  solution  ions  of  the  .metal,  the 
•elative  electrostatic  field  in  the  solution  has  already  been  par- 
ially  established,  fewer  ions  will  escape  from  the  metal  and  the 
netal  is  left  more  positive. 

Therefore  the  higher  the  concentration  of  the  positive  metallic 
ons  in  the  solution  the  more  positive  will  be  the  charge  on  the 
netal  and,  conversely,  the  lower  the  concentration  of  the  metallic 
ons  in  the  solution  the  more  negative  will  be  the  charge  on  the 
aetal. 

151 


152  THE   DETERMINATION    OF   HYDROGEN    IONS 

Not  only  metals  but  various  gases  are  found  to  act  in  a  similar 
way  when  means  are  devised  to  bring  them  into  a  situation  as 
easily  handled  as  are  metal  electrodes.  Hydrogen  is  one  of  these 
gases  and  the  means  of  handling  it  as  an  electromotively  active 
gas  is  to  take  it  up  in  one  of  those  metals  such  as  platinum,  pal- 
ladium or  iridium  which  in  a  finely  divided  condition  hold  large 
quantities  of  hydrogen.  Platinum  black  deposited  upon  plati- 
num and  laden  with  hydrogen  forms  a  hydrogen  electrode.  It 
can  be  brought  into  equilibrium  with  hydrogen  ions  as  silver  is 
brought  into  equilibrium  with  silver  ions;  and  the  more  positive 
it  becomes  the  higher  must  be  the  concentration  of  the  positively 
charged  hydrogen  ions  in  the  surrounding  solution. 

It  remains  however  to  formulate  with  mathematical  precision 
the  way  in  which  the  potential  of  the  hydrogen  electrode  changes 
with  the  concentration  of  the  hydrogen  ions;  and  for  this  purpose 
the  energy  relations  must  be  considered. 

Suppose  a  metal  electrode  dips  into  a  solution  of  ions  of  the 
same  metal.  Let  the  concentration  of  these  ions  be  such  that 
their  partial  pressure,  which  would  be  manifest  in  an  arrangement 
for  producing  osmotic  pressure,  is  P  in  the  volume  V. 

Let  the  electrode  be  of  such  a  size  that  one  gram  mol  of  ions, 
carrying  nF  faraday  of  electricty,  can  pass  from  electrode  to 
solution  to  there  raise  the  partial  pressure  by  dP.  The  increase  of 
the  difference  of  potential  between  electrode  and  solution  will  be 
dE.  The  electrical  work  expended  will  then  be  nFdE  and  the 
work  taken  up  by  the  material  system  will  be  VdP.  If  the 
process  is  reversible,  and  the  system  is  allowed  to  return  to  the 
original  state, 

nFdE  -  VdP  =  0 

VdP 
or  dE  =  -^=-.  (26) 

nF 

We  shall  now  assume  that  we  are  dealing  with  an  "ideal  solu- 
tion" by  which  we  mean  a  solution  in  which  the  pressure-volume 
relation  of  the  ions  conforms  to  the  gas  law  for  a  "perfect  gas," 

T>rp 

then  PV=RT  or  V  =  -p  . 


THEORY   OF   THE   HYDROGEN   ELECTRODE  153 

Substituting  this  equivalent  of  V  in  equation  (26)  we  have 

dE  =  5T  dP 
nFP 

On  integration  this  becomes 

E  =  — InP  +  K  (27) 

nF 

where  In  is  the  symbol  for  natural  logarithm  to  the  base  e  and  K 
is  an  integration  constant. 

The  integration  constant  is  the  point  of  reference  for  the  gen- 

TJT 
eral  relation  E  =  —  In  P.     It  is  the  potential  difference  between 

nF 

electrode  and  solution  when  some  arbitrary  unit  of  pressure 
is  chosen  and  P  =  1.  Then  in  accordance  with  the  unit  chosen 
E  =  K. 

LeBlanc  (1907)  and  others  have  substituted  for  K  an  equiv- 

T»T 

alent  constant  of  the  form  — In  p,  called  p  the  electrolytic 

nF 

solution  tension  of  Nernst  and  so  obtained  the  relation 

E  =  In  — 

nF       p 

But  it  is  of  doubtful  value  to  postulate  the  physical  signifi- 
cance of  K  in  this  manner.  For  present  purposes  we  can  afford 
to  leave  K  as  it  stands,  a  pure  integration  constant. 

Let  us  consider  now  the  arrangement  known  as  a  concentration 
cell.  Let  the  two  vessels  of  figure  13  contain  the  same  metal  ion 
in  concentrations  C  and  C  corresponding  to  "osmotic  pressures" 
P  and  P'.  Let  there  dip  into  each  solution  an  electrode  of  the 
metal.  Let  the  two  solutions  be  connected  by  a  siphon,  and  the 
slectrodes  by  a  device  for  measuring  the  E.  M.  F. 

Using  the  equation  (27)  developed  above  we  know  that  at  elec- 

T?T 
;rode  1  there  will  be  a  difference  of  potential  E  =  —  In  P  +  K  and 

nF 
PT 
it  electrode  2  a  difference  of  potential  E'  =  —  In  P'  +  K.    The 

nF 


154  THE    DETERMINATION   OF   HYDROGEN   IONS 

total  E.  M.  F.  will  be  the  algebraic  sum  of  these  potential  dif- 
ferences. If  P'  be  less  than  P,  the  electrode  in  contact  with  the 
ions  at  partial  pressure  P'  will  be  negative  to  the  electrode  in 
contact  with  the   ions  at  partial  pressure  P.     Hence 

E.M.F.  =  E-E'=  —  lnP  +  K-T—  lnP'  +  K~|=  —In-- 
nF  LnF  J      nF       P' 

Since  the  ratio  of  the  pressures  may  be  considered  equal  to  the 
ratio  of  the  ion  concentrations, 

E.  M.  F.  =  —  In  -  (28) 

nF      C 

This  is  the  fundamental  equation  for  the  E.  M.  F.  of  a  concen- 
tration chain. 

R  is  the  gas  constant,  T  the  absolute  temperature,  (273.09+ 
t  centigrade),  n  the  valency  of  the  ion  and  F  the  faraday  or  the 
quantity  of  electricity  associated  with  1  gram  molecule  equivalent. 

To  put  this  equation  into  working  form  there  have  to  be  found 
the  electrical  equivalents  for  R  and  F.  Since  measurements  of 
potential  are  to  be  made  in  terms  of  the  international  volt  this  and 
the  related  units  will  first  be  denned  as  they  are  given  in  Bureau 
of  Standards  Circular  No.  60  (1916),  "Electrical  Units  and 
Standards." 

International  ohm.  The  international  ohm,  which  is  generally 
referred  to  as  the  ohm,  but  which  is  to  be  distinguished  as  are 
other  international  units  from  the  " absolute"  units,  is  denned  as 
"the  resistance  offered  to  an  unvarying  electric  current  by  a  col- 
umn of  mercury  at  the  temperature  of  melting  ice,  14.4521  grams 
in  mass,  of  a  constant  cross-sectional  area  and  of  a  length  of 
106.300  cm." 

International  ampere.  The  international  ampere,  generally  re- 
ferred to  as  the  ampere,  is  defined  as  "the  unvarying  electric  cur- 
rent which,  when  passed  through  a  solution  of  nitrate  of  silver 
in  water  in  accordance  with  specification  II  (of  the  1908  London 
Conference),  deposits  silver  at  the  rate  of  0.00111800  of  a  gram 
per  second." 

International  volt.     The  volt  is  derived  from  current  and  re- 

E 
sistance  in  accord  with  Ohm's  law,  C  =  — .    The  international 


THEORY   OF   THE    HYDROGEN   ELECTRODE  155 

volt  is  therefore  denned  as  "the  electrical  pressure  (electromotive 
force)  which,  when  steadily  applied  to  a  conductor  the  resistance 
of  which  is  one  international  ohm,  will  produce  a  current  of  one 
international  ampere." 

F,  the  faraday,  is  derived  for  the  international  system  as  fol- 
lows. The  international  ampere  deposits  silver  at  the  rate  of 
0.00111800  of  a  gram  per  second.  Since  the  atomic  weight  of 
silver  is  107.88,  a  gram  equivalent  would  be  deposited  in  one  sec- 
ond by  96494  amperes.  The  coulomb  (international)  is  the  quan- 
tity of  electricity  transferred  by  a  current  of  one  international 
ampere  in  one  second.  Hence  96494  coulombs  are  carried  by  a 
gram  equivalent  of  silver  and  this  is  the  value  of  the  faraday  in  the 
international  system.1 

Returning  now  to  equation  (28)  we  know  that  R,  the  gas  con- 
stant, is  derived  from  the  gas  equation 

P  V  P  V 

PV  =  -£ili  T,  where  -±°12-   is  R. 

273.09  273.09 

V0,  the  volume  of  1  gram  molecule  of  an  ideal  gas  at  one  at- 
mosphere pressure  and  0°C.  is  22412  ±  2  cc.  (Berthelot,  1904). 
P0  =  one  atmosphere  or  76  cm.  of  mercury  at  0°C.  and  45°  lati- 
tude. Since  the  acceleration  of  gravity  at  45°  latitude  was  taken 
to  be  980.665  cm.  per  second  when  the  "atmosphere"  was  defined, 
and,  since  1  cc.  mercury  under  the  action  of  such  a  gravitational 
pull  weighs  13.59545  grams,  P0  =  980.665  X  76  X  13.59545  or 
1013276  dynes  per  square  centimeter. 

„  „  .    1013276X22412       ooiCWifto 

Hence  R  is =  83157719.8  ergs. 

273.09 

107  ergs  =  one  joule  absolute.  One  joule,  absolute  =  0.99966 
international  joule.  Hence  R  =  8.3129446  international  joules, 
or  volt  coulombs. 

From  the  derivations  outlined  above  our  equation  reduces  to 
the  numerical  form 

^       8.3129446  T  .    C 
E  = In  — 

96494      n       C1 
1  The  absolute  value  is  approximately  96,500  (Vinal  and  Bates,  1914). 


156  THE   DETERMINATION   OF   HYDROGEN   IONS 

Transposing  to  Briggsian  logarithms  (to  the  base  10)  by  di- 
viding by  0.43429  we  have 

E  =  0.00019837  -log  —  (29) 

n         C1 

In  the  case  of  the  hydrogen  electrode,  where  the  valence  of  the 
ionic  hydrogen  concerned  is  one,  n  is  generally  not  written. 

A  table  of  the  values  of  0.00019837  T  for  various  tempera- 
tures is  given  in  the  Appendix. 

The  significance  of  the  equation  for  the  concentration  chain  is 
that,  if  T  is  known,  and  if  the  concentration  of  the  ions  in  the 
other  solution  is  known,  then  the  concentration  of  the  ions  in  one 
solution  can  be  determined  from  the  E.  M.  F.  of  the  chain.  Fun- 
damentally there  is  no  other  way  of  applying  electromotive  force 
determinations  to  the  estimation  of  ion  concentrations,  unless 
there  can  be  brought  to  bear  mass  action  relations.  This  makes 
it  necessary  to  start  somewhere  in  the  system  with  a  solution 
whose  hydrogen  ion  concentration  has  been  determined  by  an 
independent  method. 

Let  us  assume  for  the  moment  that  the  conductivity  method 
will  give  us  correct  information  upon  the  hydrogen  ion  concen- 
tration of  some  simple  solution  such  as  that  of  HC1. 

It  will  be  remembered  that  hydrogen  ion  concentrations  are 
expressed  in  terms  of  normality,  a  solution  normal  with  respect 
to  hydrogen  ions  being  one  which  contains  in  one  liter  of  solu- 
tion 1  gram2  of  hydrogen  ions. 

If,  then,  the  normality  of  the  hydrogen  ion  concentration  in 
any  unknown  solution  is  to  be  determined  it  would  seem  that 
the  most  convenient  solution  with  which  to  compare  the  unknown 
would  be  a  solution  of  normal  hydrogen  ion  concentration.  Be- 
tween a  hydrogen  electrode  in  this  standard  and  a  hydrogen  elec- 
trode in  the  unknown  solution  of  hydrogen  ion  normality  Cx 
there  would  be  a  difference  of  potential,  E,  given  by  the  equation 

E  =  0.000, 19837  T  log  -^  (30) 

Cx 

2  It  makes  little  difference  whether  we  regard  the  atomic  weight  of 
hydrogen  as  1.0  or  as  1.008  for  the  purpose  at  hand. 


THEORY   OF   THE   HYDROGEN   ELECTRODE  157 

A  measurement  of  E  and  T  would  give  Cx.  Now  E  in  the 
above  equation  is  the  difference  between  the  potential  difference 
at  the  one  hydrogen  electrode  and  the  potential  difference  at 
the  other  hydrogen  electrode.  Nothing  need  be  known  about 
the  value  of  either  single  potential  difference  and  very  little  is 
known.  If  the  electrode  in  the  normal  solution  is  made  the 
standard  it  is  obviously  convenient  for  present  purposes  to  call 
the  potential  difference  between  this  electrode  and  the  solution 
zero.  Thus  arises  the  definition:  The  'potential  difference  between 
a  hydrogen  electrode  under  one  atmosphere  pressure  of  hydrogen  and  a 
hypothetical  solution  normal  with  respect  to  the  hydrogen  ion  shall 
be  considered  to  be  zero  at  all  temperatures} 

Having  established  by  definition  the  value  of  the  potential 
difference  at  the  normal  hydrogen  electrode  it  becomes  convenient 
to  speak  of  the  potential  difference  at  any  other  hydrogen  elec- 
trode as  the  hydrogen  electrode  potential,  thus  abbreviating  the 
term  "potential  difference."  It  is,  of  course,  implied  that  such 
a  "potential"  is  referred  to  the  potential  difference  at  the  normal 
hydrogen  electrode.     To  indicate  this  the  symbol  Eh  is  used. 

Unfortunately  it  has*  been  necessary  to  introduce  into  the 
definition  of  the  normal  hydrogen  electrode  the  phrase  u  hy- 
pothetical solution  normal  with  respect  to  the  hydrogen  ion." 
This  is  because  that  very  desirable  standard  solution  would  have 
to  be  prepared  by  means  of  "strong"  acids  and  the  estimation 
of  the  hydrogen  ion  concentration  would  fall  under  those  uncer- 
tainties which  have  already  been  mentioned  in  a  previous  chapter. 
The  difficulty  is  not  entirely  obviated  by  making  the  experimental 
standard  a  more  dilute  solution  of  a  strong  acid  as  has  been  done; 
but  we  shall  leave  to  Chapter  XIX  further  discussion  of  this 
Droblem,  and,  for  the  moment,  we  shall  assume  that  there  can  be 
constructed  from  measurements  such  as  those  of  the  conductivity 
nethod  a  solution  having  a  definite,  known  hydrogen  ion  con- 
centration. We  could  proceed  with  this,  using  it  as  one  of  two 
iolutions  in  a  hydrogen  gas  cell,  and  applying  to  this  cell  the 

3  In  various  places,  notably  in  the  report  of  the  Potential  Commission 
>f  the  Bunsen-Gesellschaft  (Abegg,  Auerbach  and  Luther,  1910)  it  is  not 
pecifically  stated  that  this  difference  of  potential  shall  be  zero  at  all  tem- 
peratures, but  it  seems  to  have  been  so  understood  and  is  specifically  so 
;  tated  by  Lewis  (1913). 


158  THE   DETERMINATION   OF   HYDROGEN   IONS 

formula  relating  the  E.  M.  F.  to  the  ratio  of  the  known  to  the 
unknown  hydrogen  ion  concentration.  But  it  is  more  convenient 
to  use  as  a  working-standard  a  calomel  half  cell  (see  Chapter 
XIII).  When  this  is  joined  to  a  hydrogen  electrode  to  form  a 
calomel-hydrogen  cell  we  need  to  know  the  difference  of  poten- 
tial between  the  calomel  half  cell  and  some  known  hydrogen  elec- 
trode. Then  we  can  correct  the  observed  E.  M.  F.  by  this  differ- 
ence and  consider  the  corrected  E.  M.  F.  to  be  as  if  it  were  that 
between  two  hydrogen  electrodes. 

Remembering  that  the  mercury  of  the  calomel  half  cell  is  posi- 
tive to  the  platinum  of  the  normal  hydrogen  electrode  and  that 
the  platinum  of  a  hydrogen  electrode  becomes  more  negative 
the  more  dilute  the  hydrogen  ion  concentration,  we  have  the  scheme 
shown  below 


8  a 

O       O  ml 

p,  a  ai    Total 
3  *    "'  E.M.F. 

o  JS 

J  .2 

<  * 


-Mercury  of  calomel  electrode 

Eh  of  calomel  electrode 
— Pt  of  normal  hydrogen  electrode 
Ehx  of  hydrogen  electrode  X 

-Pt  of  fractional  normal  hydrogen 
electrode  X 


If  E.  M.  F.  is  measured  and  Eh  is  known,  the  value  of  Ehx 
is  at  once  obtained.  This  is  the  difference  of  potential  between 
two  hydrogen  electrodes  and  equation  (29)  applied.  In  its  work- 
ing form  this  equation  is: 

E.M.F.  (observed)  -  Eh  (of  calomel  half  cell)  _  .        1     =    H  ,^s 
0.000,198,37T  ~        [H+] 

The  above  equation  is  still  incomplete  because  we  have  not  taken 
into  consideration  the  liquid  junction  potential  differences  which 
exist  wherever  two  unlike  solutions  are  brought  into  contact.  Nor 
have  we  yet  considered  the  effect  upon  the  potential  difference  at  a 
hydrogen  electrode  of  a  change  in  the  pressure  of  hydrogen  from 
the  one  atmosphere  partial  pressure  specified  for  the  normal  hy- 
drogen electrode.  These  two  will  be  considered  from  the  point 
of  view  of  corrections  to  be  made.  Liquid  junction  potential 
differences,  because  of  their  distinct  importance,  will  be  treated 
in  a  separate  chapter. 


THEORY    OF   THE    HYDROGEN    ELECTRODE  159 


BAROMETRIC    CORRECTION 

The  potential  difference  between  a  metal  and  solution  will 
vary  somewhat  with  the  condition  of  the  metal.  A  hammered, 
twisted  or  scratched  electrode  may  show  a  different  potential 
against  a  given  concentration  of  its  ions  than  will  an  electro- 
lytically  deposited  metal.  In  the  case  of  the  hydrogen  electrode 
it  seems  to  make  little  difference  whether  the  hydrogen  be  held 
in  platinum,  palladium  or  iridium  but  it  does  make  a  consider- 
able difference  if  the  surrounding  pressure  of  hydrogen  varies.  If 
we  have  two  hydrogen  electrodes  immersed  in  the  same  solution 
at  the  same  temperature  but  under  different  pressures  of  gaseous 
hydrogen,  we  may  assume  that  the  concentration  of  the  hydrogen 
in  one  electrode  is  different  from  that  in  the  other  electrode,  and 
that  the  potential  difference  may  be  expressed  as 

E  =  Ex-E2=  —  ln[-5li  (32) 

nF       [H]2 

in  which  equation  R,  T,  n,  and  F  have  their  customary  signifi- 
cances and  [H]i  and  [H]2  are  concentrations  of  atomic  hydrogen  in 
the  electrodes  (platinum  black).  Since  n,  the  valence  of  hydro- 
gen, is  1,  it  may  be  omitted. 

We  may  now  assume  that  there  is  an  equilibrium  between  the 
molecular  hydrogen  about  the  electrode  and  the  atomic  or  ionic 
hydrogen  in,  or  issuing  from,  the  electrode.  This  equilibrium 
may  be  expressed  in  accordance  with  the  mass  law  as  follows : 

rxr]  y  rTTl 

—  =  Kt    where  [H]  =  concentration  of  atomic  hydrogen 

[H2] 

and  [H2]  =  concentration  of  molecular  hydrogen 

Whence, 

[H]  =  VkS]  (33) 

Substituting  (33)  in  (32),  we  have 

E-  RT  ln  VKOH^  _  RT^tH^ 
F        VKt[H2]2  "  2F       [H2]2 

It  should  be  noted  that  the  factor  2  in  this  equation  does  not 
:ome  from  giving  hydrogen  an  effective  valence  of  2,  as  has  often 
)een  stated,  but  from  the  introduction  of  equation  (33).     We 


160  THE   DETERMINATION   OF   HYDROGEN   IONS 

might  however  derive  the  equation  more  directly  by  the  energy 
relations  and  then  the  factor  2  would  enter  by  reason  of  the  vol- 
ume change  involved. 

If  the  ratio  of  pressures  is  equal  to  the  ratio  of  gas  concentrations 

E  =  — ln^? 
2F       PH2 

If  P'H,  be  one  atmosphere  and  PH2  be  expressed  in  atmospheres 

tp       RT,      1 

E  =  In  —  ,OA, 

2F       PH1  (34) 

This  is  the  equation  for  the  difference  of  potential  between  a 
hydrogen  electrode  under  one  atmosphere  pressure  of  hydrogen 
(e.g.,  the  normal  hydrogen  electrode)  and  a  hydrogen  electrode 
under  pressure  PH2. 

Experimental  justification  of  this  equation  is  found  in  the 
experiments  of  Czepinski,  Lewis  and  Rupert,  Lewis  and  Randall, 
Lewis  and  Sargent,  Ellis,  Loomis  and  Acree  and  others. 

Hainsworth  and  Maclnnes  have  studied  the  effect  of  pressures 
up  to  400  atmospheres  and  taking  account  of  the  volume  changes 
of  Hg,  calomel,  etc.  which  are  negligible  for  smaller  differences 
in  pressure,  they  find  a  linear  relation  except  for  a  slight  deviation 
at  the  higher  pressures. 

Several  writers  have  felt  constrained  to  emphasize  the  fact  that 
in  determining  the  hydrogen  pressure  from  barometer  readings 
they  have  subtracted  the  vapor  pressure  of  the  solution.  The 
emphasis  is  still  advisable,  for  a  considerable  number  of  precise 
hydrogen  electrode  data  are  published  with  corrections  for  baro- 
metric pressure  on  the  basis  that  the  normal  hydrogen  electrode 
pressure  is  one  atmosphere  including  the  vapor  pressure  of  the 
solution.  Corrections  should  be  made  to  one  atmosphere  pres- 
sure of  hydrogen,  or  else  the  standard  used  should  be  distinctly 
specified. 

Clark  and  Lubs  (1916)  have  suggested  that  a  more  consistent 
standard  than  that  now  recognized  for  the  normal  hydrogen  elec- 
trode would  be  obtained  by  defining  a  standard  concentration  of 
hydrogen  father  than  a  standard  pressure.  They  used  the  com- 
monly accepted  "standard  condition"  of  a  gas  which  is  the  con- 


THEORY   OF  THE   HYDROGEN   ELECTRODE  161 

centration  at  0°C.  and  760  mm.  pressure.     This  would  bring  both 
the  hydrogen  and  the  hydrogen  ions  to  a  concentration  basis, 
whereas  now  the  one  is  expressed  in  terms  of  concentration  and 
the  other  in  terms  of  pressure. 
In  applying  the  correction, 

T?  RT,       1 

Ebar. m 


2F        PH, 

it  will  be  remembered  that  a  decrease  of  the  hydrogen  pressure 
may  be  considered  as  a  decrease  of  the  electrolytic  solution 
tension  of  the  hydrogen.     Hence  under  decreased  hydrogen  pres- 
sure the  electrode  is  left  more  positive. 
In  the  cell 

Hg  |  Hg2Cl2KCl  |  H+  |  Pt  |  H2 

if  the  hydrogen  is  under  diminished  pressure  the  E.  M.  F.  of  the 
cell  is  too  low.  Hence  the  correction  must  be  applied  to  make  the 
E.  M.  F.  larger  than  observed.     Equation  (31)  becomes: 

E.  M.  F.  +  E(bar.)   —      E(caiome])     __       jt  (ok) 

.0.00019837  T 

To  aid  in  the  calculation  of  pressure  corrections  it  is  convenient 
to  plot  a  curve  giving  the  millivolts  to  be  added  to  the  observed 
E.  M.  F.  for  various  corrected  partial  pressures.  Tables  of  correc- 
tions from  which  a  chart  may  be  plotted  are  given  in  the  Appen- 
dix. In  these  tables  the  barometer  pressures  given  are  the  cor- 
'ected  pressures.  If  hydrogen  escapes  from  about  the  hydrogen 
ilectrode  through  a  trap  or  other  device  which  exerts  back  pres- 
sure, this  pressure  must  be  taken  into  consideration.  Otherwise 
t  is  assumed  that  the  pressure  of  the  hydrogen  is  that  of  the 
urometer  less  the  vapor  pressure  of  the  solution.  To  obtain  the 
orrected  barometer  reading  the  instrumental  calibration  of  the 
instrument  is  first  applied,  then  the  temperature  correction  (a 
■  able  of  which  is  given  in  the  Appendix)  necessary  to  bring  the 
1  eight  of  the  mercury  column  at  temperature  t  to  its  height  at 
1  amperature  0°C.  Then  there  remains  the  correction  for  locality 
( see  tables  in  Landolt-Bornstein)  in  order  that  the  pressure  may 
1  e  reduced  to  the  common  basis  of  the  "atmosphere,"  namely,  the 
I  ressure  of  760  mm.  mercury  where  the  acceleration  of  gravity  is 


162  THE    DETERMINATION    OF   HYDROGEN   IONS 

980.665  cm.  per  second.  The  last  correction  is  of  significance 
only  for  very  accurate  measurements  and  exceptional  localities. 

For  all  ordinary  cases  it  may  be  assumed  that  the  vapor  pres- 
sure is  that  of  pure  water  at  the  temperature  indicated. 

If  the  unit  pressure  is  one  atmosphere,  the  partial  pressure 
must  be  reduced  to  atmospheres. 

As  inspection  of  the  table  in  the  Appendix  will  indicate,  the 
barometric  correction  may  be  neglected  in  rough  measurements. 

REFERENCES 
General 

Abegg-Auerbach-Luther  (1911),  Bose  (1900),  Carhart  (1911),  Fresenius 
(1912),  Foa  (1906),  Hardman-Lapworth  (1911-12),  Jahn  (1901), 
Kistiakowsky  (1908),  Lewis,  G.  N.  (1908,  1913),  Lewis-Randall 
(1914),  Lewis,  W.  K.  (1908),  Loven  (1896),  Michaelis  (1910,  1911, 
1914),  Myers-Acree  (1913),  Nernst  (1889,  1916),  Nernst-Wilsmore 
(1900),  Noyes,  Ostwald  (1891),  Rothmund  (1894),  Smale  (1894), 
Stieglitz   (1917),  Wilsmore  (1900). 

Gas  Constant,  R 
Berthelot  (1904),  Nernst  (1904),  Van  Laar  (1893,  1921). 

Value  of  the  faraday 

Vinal-Bates  (1914). 

Barometer  correction 

Bose  (1900),  Czepinski  (1902),  Ellis  (1916),  Foa  (1906),  Hainsworth-Mac- 
Innes  (1922),  Lewis,  W.  C.  (1920),  Lewis-Randall  (1914),  Lewis- 
Rupert  (1911),  Lewis-Brighton-Sebastian  (1917),  Loomis  (1915), 
Loomis-Acree  (1916),  Loomis-Myers-Acree  (1917),  Ostwald  (1893), 
Smale  (1894),  Wilsmore  (1901),  Wulf  (1904). 

Condition  of  hydrogen  in  electrodes  and  catalytic  activation 

Berry  (1911),  Eggert  (1915),  Freeman  (1913),  Harding-Smith  (1918), 
Hemptinne  (1898),  Hoitsema  (1895-6),  Holt  (1914),  Holt-Eggar-Firth 
(1913),  LeBlanq  (1893),  Luther-Brislee  (1903),  Maxted  (1919-1921), 
Mond-Ramsay-Shields  (1898),  Winkelmann  (1901). 

Null  point  of  potential 

Abegg-Auerbach-Luther  (1909-1911),  Brunner  (1909),  Freundlich-Makelt 
(1909),  Goodwin-Sosman  (1905),  Lorenz  (1909),  Lorenz-Mohn  (1907), 
Nernst  (1897),  Ostwald  (1900),  Palmaer  (1898,  1907),  Wilsmore- 
Ostwald  (1901). 


CHAPTER  XI 
Potential  Differences  at  Liquid  Junctions 

When  two  unlike  solutions  of  electrolytes  are  brought  into  con- 
tact there  develops  at  the  junction  a  potential  difference.  Since 
no  important  chain  can  be  constructed  without  involving  such  a 
liquid  junction  potential,  it  is  of  great  importance  to  know  the 
cause  so  that  the  magnitude  of  the  potential  may  be  calculated 
or  ways  devised  for  its  reduction. 

The  principal  cause  of  the  potential  difference  was  attributed 
by  Nernst  to  unequal  rates  of  diffusion  of  ions  across  the  plane 
of  junction. 

It  has  been  found  in  the  study  of  electrolytic  conduction  that 
under  uniform  potential  gradient  different  ions  move  through  a 
solution  with  different  velocities.  The  following  table  taken  from 
Lewis'  A  System  of  Physical  Chemistry  shows  the  velocities  of  a 
number  of  ions  in  aqueous  solution  under  a  potential  gradient 
of  one  volt  per  centimeter.  Since  in  each  case  the  potential  gra- 
dient is  the  same  and  the  ionic  charge  the  same  it  is  evident  that 
the  order  in  which  the  velocities  stand  in  the  table  is  the  order 
in  which  the  velocities  of  free  movement  will  stand. 


ION 

ABSOLUTE  VELOCITY 

IN  CENTIMETERS  PER 

SECOND.      18°C. 

ION 

ABSOLUTE  VELOCITY 

IN  CENTIMETERS  PER 

SECOND.      18°C. 

H 

32.50  10"* 
6.70  10"* 
4.51  10-* 
3.47  10"* 
5.70  10"* 

OH 

17.80  10~* 

K 

CI 

6.78  10"* 

Na 

N03 

6.40  10-* 

Li 

CHsCOO 

3.20  lO-4 

Ag 

Let  it  now  be  assumed  that  a  solution  of  hydrochloric  acid  is 
placed  in  contact  with  pure  water  of  negligible  ion  content  at  an 
imaginary  plane  surface.  Independently  of  one  another  the 
ihlorine  and  the  hydrogen  ions  will  tend  to  migrate  across  the  inter- 
'ace  and  into  the  water.  As  shown  in  the  above  table  the  velocity 
)f  the  hydrogen  #ion  under  the  influence  of  a  potential  gradient 

163 


164  THE   DETERMINATION    OF   HYDROGEN   IONS 

is  much  greater  than  the  velocity  of  the  chlorine  ion  under  the 
same  gradient,  and  the  relative  velocities  of  free  movement  must 
therefore  be  in  the  same  proportion.  Consequently  there  will 
be  established  on  the  water  side  of  the  plane  an  excess  positive 
charge.  This  charge  will  increase  until  the  electrostatic  attrac- 
tion dragging  the  slower  moving  chlorine  ions  brings  them  to  the 
velocity  of  the  hydrogen  ions.  When  this  state  is  reached,  as  it 
is  almost  instantaneously,  there  is  established  a  steady  potential 
difference  at  the  liquid  junction.  If  the  water  is  replaced  by  a 
solution  of  an  electrolyte,  we  have  not  only  the  chlorine  and  the 
hydrogen  ions  migrating  across  the  boundary  into  this  new  solu- 
tion, but  the  ions  of  this  solution  migrating  into  the  hydrochloric 
acid  solution. 

In  the  comparatively  simple  case  where  two  solutions  of  differ- 
ent concentration  of  the  same  binary  electrolyte  are  placed  in 
contact  the  following  elementary  treatment  may  be  used.  Let 
the  concentration  of  the  ions  on  one  side  of  the  interface  be  C 
and  on  the  other  side  be  a  lesser  concentration  C 

When  migration  has  established  the  steady  potential  E  let  it 

be  over  an  interface  of  such  extent  that  E  is  due  to  the  separation 

of  one  faraday.     If  that  fraction  of  the  separated  charge  which 

is  carried  by  the  anion  is  na  the  work  involved  in  the  transport  of  na 

C  . 

equivalents  from  C  to  C  is  na  RT  In  ^>.  Likewise  if  that  fraction  of 

the  charge  carried  by  the  cations  is  nc  the  work  involved  in  the 

C 

transport  of  nc  equivalents  from  C  to  C  is  nc  RT  In  p7,.     The 

work  involved  in  the  separation  of  the  ions  as  they  migrate  from 
the  high  to  the  low  concentration  is 


naRTln—  -  ncRTln—  =  EF 

c  c 


Whence 


E  =  (n.  -  nc)  —  In  —  or  (n0  -  na)  —-In  —  (36) 

F        C  r         C 

according  to  which  ion  moves  the  faster. 

Now  the  ions  being  univalent,  na,  the  fraction  of  the  charge  car- 
ried by  the  anion,  is  equal  to  the  fraction  N  of  one  equivalent  of 
anions  transported  from  the  cathode  to  the  anode  section.     Like- 


POTENTIAL   DIFFERENCES    AT   LIQUID    JUNCTIONS 


165 


wise  n0  is  1-N.     The  ratio  of  N  to  1-N  is  equal  to  the  ratio  of 
the  absolute  velocities  of  the  ions. 

N         velocity  of  anion  (Va) 


1  —  N      velocity  of  cation  (Vc) 


Whence 


and 


N  = 


Va  +  V, 


1-N  = 


Va  +  V, 
Substituting  N  for  na  and  1 


,  transport  number  of  anion, 


,  transport  number  of  cation. 
N  for  nc  in  equation  (36) 


E=(Va_-LVe)    RTlnC 
(Va  +  V0)     F       C 


(37) 


Lewis  and  Sargent  (1909)  have  treated  the  special  case  of  two 
equally  concentrated  solutions  of  two  binary  salts  having  one  ion 
in  common.  Substituting  equivalent  conductivities  as  propor- 
tional to  mobilities  they  obtain 


E^ln^i 
F        X2 


(38) 


where  Xi  and  X2  are  the  equivalent  conductivities  of  two  solu- 
tions. Applying  this  equation  they  obtain  the  following  corre- 
spondence between  calculated  and  observed  values  of  E,  the 
liquid  junction  potential. 


SOLUTIONS  IN  CONTACT 

E (observed) 

E  (calcu- 
lated) 

E  (OBS.)- 
E  (CALC.) 

).2nKC1-0  2nKC2H30, 

).1nKC1-0.1n  KC2H302 

).2nKC1-0.2n  KOH 

-0.0080 
-0.0074 
+0.0170 
+0.0165 
+0.0004 
+0.0192  ±0.0003 
-0.0286 

-0.0082 
-0.0077 
+0.016S 
+0.0165 
+0.0004 
+0.0187 
-0  0286 

0.0002 
0.0003 
0.0002 

).1nKC1-0.1nKOH 

0.0000 

).2n  KC1-0.2n  KBr 

0.0000 

).2n  NuC1-0.2n  NaOH 

I. In  KCI-O.In  HC1 

0.0000 

In  the  more  general  case  limited  chiefly  by  the  condition  that 


166  THE   DETERMINATION    OF   HYDROGEN   IONS 

all  the  ions  shall  have  the  same  valency  Planck  (1890)  deduced 
the  equation: 

E  -  5^  ln  ^  (39) 

wF 

where  E  is  the  contact  difference  of  potential  in  volts  and  £  is 
defined  by  the  equation: 

ln?-2-ln£ 
SU2  -  Ui  m      C!  i  gc2  -  ci 

V*-^      In^  +  ln/02"^1 

Ci 

Ci  is  the  sum  of  the  concentrations  of  cations  and  anions  in  the 
more  dilute  solution  and  c2  the  sum  in  the  more  concentrated  solu- 
tion,    w  is  the  valency,  R  the  gas  constant,  F  the  faraday,  and 

Ui  =  uV  +  u"c"  +  .  .  .  . 
V,  =  vV  +  v"c"  +  .  .  .  . 

and  U2  and  V2  are  similar  sums  for  the  second  solution.  The  u' 
and  v'  symbols  represent  the  ion  mobilities  and  the  c'  symbols 
the  corresponding  ion  concentrations. 

Besides  the  limitation  noted  above  this  equation  is  strictly  ap- 
plicable only  to  very  dilute  solutions  where  dissociation  is  complete 
and  it  was  deduced  for  the  condition  of  a  sharp  boundary  such 
as  is  not  realized  in  experimental  work. 

P.  Henderson  (1907,  1908)  therefore  considered  the  connecting 
boundary  as  a  series  of  mixtures  of  the  two  solutions  in  all  propor- 
tions and  deduced  a  somewhat  simpler  equation  which  Cumming 
(1912)  has  modified  by  introducing  the  mobilities  at  the  different 
concentrations  used. 

It  is  of  course  obvious  that  the  equations  given  above  and  many 
others  of  like  nature  are  inapplicable  when  the  solutions  placed 
in  contact  are  of  unknown  composition  or  are  very  complex. 
Br0nsted  (1922)  has  proposed  a  novel  method  of  approach  which 
may  prove  to  have  some  value,  but  as  yet  it  is  untried,  and  we 
are  forced  to  get  such  comfort  as  we  can  find  in  a  deduction  from 
the  above  treatment  which  will  be  considered  presently.  But 
even  in  the  simple  cases  where  one  or  another  of  the  equations 


POTENTIAL  DIFFERENCES   AT  LIQUID   JUNCTIONS  167 

apply  the  experimenter  must  face  the  difficulty  of  maintain- 
ing experimentally  the  conditions  for  which  they  were  set  up. 
For  instance  Chanoz  (1906)  constructed  the  symmetrical 
arrangement : 

Electrode  II  MR  I  M'R'  I  MR  II  Electrode, 
A  B 

and  then,  by  maintaining  a  more  or  less  sharp  boundary  at  A  by 
renewal  of  the  contact,  and  allowing  diffusion  to  occur  at  B,  he 
obtained  very  definite  E.  M.  F.'s  instead  of  the  zero  E.  M.  F. 
which  the  symmetrical  arrangement  demanded.  This  time  effect 
has  been  noted  by  Weyl  (1905)  and  has  since  been  frequently 
reported,  for  instance,  by  Bjerruni  (1911),  Lewis  and  Rupert 
(1911),  Cumming  and  Gilchrist  (1913),  Walpole  (1914)  andFales 
and  Vosburgh  (1918). 

Since  the  change  of  potential  has  been  ascribed  to  the  diffusion 
and  mixing  which  alter  the  distribution  of  the  contending,  mi- 
grating ions,  it  has  seemed  to  many  that  the  effect  could  be  made 
more  uniform  and  conditions  more  reproducible  if  the  solutions 
were  brought  into  contact  at  a  membrane.  This  would  tend  to 
prevent  mixing.  Sand  or  other  material  would  also  delay  the 
mixing  and  the  diffusion.  Cumming  and  Gilchrist  (1913)  used 
a  symmetrical  chain  such  as  that  of  Chanoz  (see  above) ,  and  found 
that  when  a  membrane  was  introduced  at  A  while  ordinary  con- 
tact was  allowed  at  B  the  symmetry  of  the  chain  was  destroyed. 
Prideaux  (1914)  also  found  a  difference  when  the  contact  was 
made  in  the  one  case  with,  and  in  the  other  case  without,  a  parch- 
ment membrane.  On  considering  this  case  and  others  in  which 
the  constituents  of  the  membrane  may  take  part  in  the  establish- 
ment of  the  potential,  he  came  to  the  conclusion  that  there  were 
phenomena  concerned  which  made  the  application  of  the  ordinary 
squations  of  dubious  value.     See  also  Beutner  (1913). 

Lewis,  Brighton  and  Sebastian  (1917)  using  Bjerrum's  (1911) 
suggestion  of  a  layer  of  sand  in  which  to  establish  the  liquid  con- 
act  found  that  "at  no  time  were  reproducible  results  obtained 
lor  results  which  remained  constant  to  0.0001  volt  for  more  than 
i  minute  or  two.  The  potential  of  the  liquid  junction  first  es- 
ablished  was  surprisingly  high  (0.030  volt)  and  fell  rapidly  with- 


168  THE   DETERMINATION   OF   HYDROGEN   IONS 

out  reaching  any  definite  limiting  value. "  The  liquids  placed  in 
contact  in  this  experiment  were  0.1m  HC1  and  0.1m  KC1.  These 
authors  abandpned  the  sand  method. 

On  the  other  hand  Myers  and  Acree  (1913)  report  satisfaction 
with  Bjerrum's  " Sandfiillung. " 

Other  devices  such  as  the  use  of  a  wick  have  been  resorted  to, 
but  on  the  whole  direct  liquid  contact  is  considered  the  best. 

Recently  Lamb  and  Larson  (1920)  have  described  the  "flowing 
junction"  which  they  find  to  be  much  more  reproducible  than 
the  junctions  usually  made.  They  conclude  "that  a  'flowing' 
junction,  obtained  simply  by  having  an  upward  current  of  the 
heavier  electrolyte  meet  a  downward  current  of  the  lighter  elec- 
trolyte1 in  a  vertical  tube  at  its  point  of  union  with  a  horizontal 
outflow  tube,  or  by  allowing  the  lighter  electrolyte  to  flow  con- 
stantly into  a  large  volume  of  the  heavier  electrolyte,  even  with 
N  solutions,  gives  potentials  constant  and  reproducible  to  0.01  of 
a  millivolt. "  The  device  used  by  Lamb  and  Larson  is  illustrated 
in  figure  15. 

Maclnnes  and  Yeh  (1921)  have  improved  the  system  of  Lamb 
and  Larson  and  have  confirmed  the  principle  that  reproducible 
liquid  junction  potentials  may  be  thus  obtained,  but  they  find 
most  interesting  effects  with  different  rates  of  flow.  Of  particular 
importance  is  the  observation  that  the  reproducible  potentials 
are  not  the  highest  that  can  be  obtained. 

It  is  encouraging  to  see  experimental  work  of  this  type  being 
done  for  those  who  are  interested  in  the  general  applications  of 
electrode  measurements  cannot  escape  the  feeling  that  the  ex- 
perimental side  of  the  problem  has  been  too  much  neglected. 

A  most  important  contribution  to  experimental  methods  of 
handling  liquid  junction  potential  differences  arose  from  the  the- 
ory of  Nernst  that  the  potential  is  due  to  the  unequal  migration 
of  ions.  The  table  of  velocities  given  on  page  163  will  show  that 
if  KC1  is  concerned  no  large  potential  can  arise  from  the  partici- 
pation of  its  ions,  because  they  move  with  about  the  same  velocity. 
If  such  a  salt  be  present  in  high  concentration  upon  both  or  even 
one  side  of  the  interface,  the  electrostatic  fields  of  its  ions  will 
dominate  the  situation,  and,  migrating  at  equal  velocities,  will  tend 
to  maintain  zero  junction  potential  difference.  Bjerrum  (1911) 
studied  the  potential  differences  developed  when  concentrated  so- 


POTENTIAL  DIFFERENCES   AT  LIQUID   JUNCTIONS 


169 


lutions  were  thus  employed  and  estimated  the  theoretical  values 
with  the  aid  of  Planck's  formula  and  with  that  of  Henderson, 
which  purports  to  take  into  account  the  effect  of  the  destruction 
of  a  sharp  boundary.  He  came  to  the  conclusion  that  the  use 
of  a  3.5m  KC1  solution  would  not  completely  eliminate  the  po- 
tential against  hydrochloric  acid  solutions  but  he  suggested  a 
more  or  less  empirical  extrapolation  which  would,  he  thought, 


Fig.  15.  Lamb  and  Larson's  Device  for  the  Flowing  Junction 

j  ive  the  proper  correction.  The  correction  is  the  difference  in  the 
]  1.  M.  F/s  of  a  chain  found  when  first  3.5m  KC1  is  used  and  then 
>  men  1.75m  KC1  is  used  to  connect  two  electrodes. 

More  recently  Fales  and  Vosburgh  (1918)  have  made  an  ex- 
t  msive  comparison  of  various  chains,  and  with  the  aid  of  Planck's 
f  )rmula  to  give  the  order  of  magnitude  of  various  contact  poten- 
t  als,  thay  have  attempted  to  assign  values  which  will  lead  to  a 
g  3neral  consistency.  They  concur  with  others  in  finding  Planck's 
f  irmula  invalid  in  the  assignment  of  accurate  values  to  liquid 
j  motions,  such  as: 


170  THE   DETERMINATION   OF   HYDROGEN   IONS 

"xm  KC1  -  1.0m  HC1  and  xu  KC1  -  0.1m  HC1  where  x  ranges 
from  0.1  to  4.1  and  the  temperature  is  25°C." 

They  conclude  that  "there  is  no  contact  potential  difference  at 
25°  between  a  saturated  solution  of  potassium  chloride  (4.1m)  and 
hydrochloric  acid  solutions  ranging  in  concentrations  from  0.1 
molar  to  1.0  molar,"  confirming  the  suggestion  of  Loomis  and 
Acree  (1911). 

Because  of  the  great  detail  concerned  in  the  reasoning  of  Fales 
and  Vosburgh  it  is  impossible  to  briefly  summarize  their  work,  but 
before  their  conclusion  can  be  considered  valid  it  must  be  noted 
that  they  themselves  point  out  that  "in  an  electromotive  force 
combination  having  a  contact  potential  difference  as  one  of  its 
component  electromotive  forces,  the  diffusion  across  the  liquid 
junction  of  the  one  liquid  into  the  other  brings  about  a  decrease  in 
the  magnitude  of  the  contact  potential  difference,  and  this  de- 
crease may  amount  to  as  much  as  one-tenth  of  the  initial  magni- 
tude of  the  contact  potential  difference. "  This  experimental  un- 
certainty undoubtedly  renders  questionable  the  comparability, 
if  not  the  precision  of  measurements  by  different  experimenters. 
If  so  there  may  lurk  in  the  data  used  by  Fales  and  Vosburgh  in 
their  argument  of  adjustment  to  consistency  an  indefinite  degree 
of  incomparability. 

Indeed  the  whole  subject  of  contact  potential  is  still  in  an  un- 
satisfactory state.  The  experimental  uncertainties  which  have 
been  revealed  have  sometimes  been  overlooked  in  the  calculation 
of  important  electrode  values.  Some  of  these  values  will  be  dis- 
cussed in  Chapter  XIX. 

In  writing  the  components  of  a  chain  it  is  customary  to  desig- 
nate the  situation  of  a  potential  difference  by  a  single  line  and 
the  position  of  a  potential  difference  which  is  to  be  left  out  of 
consideration  by  a  double  line.     Thus 

Pt  H2 1  N/10  HC1 1  N/10  KC1  Hg2Cl2 1  Hg 

indicates  that  there  are  potential  differences  at  the  positions 
shown  by  the  lines;  while  if  the  above  chain  is  written  as 

Pt  H2 1  N/10  HC1 1|  N/10  KC1  Hg2Cl2  |Hg 

the  double  line  indicates  that  the  liquid  junction  potential  differ- 
ence is  to  be  left  out  of  consideration  in  formulating  the  E.M.F. 


POTENTIAL   DIFFERENCES   AT   LIQUID   JUNCTIONS  171 

It  now  remains  to  determine  if  possible  the  order  of  magnitude 
of  the  contact  differences  of  potential  entering  into  chains  used 
in  the  study  of  physiological  solutions  and  the  buffer  solutions  of 
the  colorimetric  method. 

Since  the  concentrations  of  the  hydrogen  and  the  hydroxyl  ions, 
which  are  the  most  mobile  of  all  ions,  are  very  low  in  most  of  these 
solutions,  the  contact  potential  difference  may  be  expected  to  be 
much  less  than  that  found  in  hydrochloric  acid  solutions  and  sim- 
ilar solutions  of  high  hydrogen  or  hydroxyl  ion  concentrations. 
It  is  the  customary  practice  to  employ  saturated  KC1  in  making 
the  junction  or  to  make  the  junction  first  with  3.5m,  then  with 
1.75m  KC1  and  extrapolate  according  to  Bjerrum.  The  extra- 
polation so  indicated  generally  amounts  to  only  a  few  tenths  of  a 
millivolt,  and  in  certain  cases  such  as  "standard  acetate"  to  only 
0.1  millivolt.  Although  such  an  extrapolation  may  be  too  low  or 
too  high  its  magnitude  indicates  that  the  error  is  not  large. 
Furthermore  there  is  found  experimentally  a  drift  in  contact 
potential  difference  with  time  which  is  very  much  less  than  that 
found,  for  instance,  at  the  junction  sat.  KC1— 0.1m  HC1.  There  can 
be  no  doubt  that  this  is  indicative  of  a  low  potential  difference. 

As  pointed  out  by  Clark  and  Lubs  (1916),  it  is  the  difficulty  in 
dealing  with  the  contact  potential  of  hydrochloric  acid  solutions 
that  renders  them  unsuitable  for  routine  standardization  of 
hydrogen  electrodes. 

Practical  conclusions  reached  by  experimentation  are: 

1.  For  precise  E.  M.  F.  measurements  combinations  having 
small  liquid  junction  differences  of  potential  should  be  used  as 
far  as  is  practicable. 

2.  It  should  be  recognized  that  the  E.  M.  F.  of  a  cell  which 
derives  part  of  its  E.  M.  F.  from  a  liquid  junction  potential  dif- 
ference varies  with  the  time  elapsing  after  the  formation  of  the 
liquid  junction.  Consequently  this  time  should  become  a  part 
of  the  data  to  be  recorded. 

3.  It  is  preferable  that  measurements  of  E.  M.  F.  be  made 
directly  after  the  formation  of  or  the  renewal  of  the  liquid  junction. 

4.  Since  the  liquid  junction  potential  difference  may  vary  with 
the  manner  of  its  formation  the  effort  should  be  made  to  effect  this 
junction  in  a  reproducible  way. 

5.  Reproducible  potential  differences  are  given  by  the  flowing 
junction  in  the  cases  so  far  tried. 


172         THE  DETERMINATION  OF  HYDROGEN  IONS 

6.  Narrow  or  capillary  tubes  at  the  point  of  liquid  junction 
should  be  avoided. 

7.  An  apparatus  which  permits  the  renewal  of  a  junction  and 
its  complete  removal  when  cells  are  left  set  up  together  for  some 
time  is  preferable  to  any  device  such  as  membranes  to  protect  the 
diffusion  of  solutions  into  electrode  spaces. 

8.  Membranes  at  the  liquid  junction  are  to  be  avoided. 

9.  Wherever  permissible  saturated  KC1  solution  should  form 
one  side  of  a  liquid  junction. 

10.  When  a  concentrated  KC1  solution  is  used  to  make  liquid 
junction  it  should  be  stated  whether  the  Bjerrum  extrapolation 
with  the  use  of  3.5m  and  1.75m  KC1  has  been  employed  or  whether 
saturated  KC1  was  used  without  the  Bjerrum  extrapolation. 

REFERENCES 

Abegg-Bose  (1899),  Beutner  (1912),  Bjerrum  (1905,  1911),  Chanoz  (1906), 
Clarke,  W.  F.-Myers-Acree  (1916),  Cremer  (1906),  Cumming  (1912), 
Cumming-Abegg  (1907),  Cumming-Gilchrist  (1913),  Donnan  (1911), 
Fales-Vosburgh  (1918),  Gouy  (1916),  Ferguson  (1916),  Henderson,  P. 
(1907-1908),  Lamb-Larson  (1920),  Lewis-Sargent  (1909),  Lewis- 
Rupert  (1911),  Loomis-Acree  (1911),  Loven  (1896),  Maclnnes  (1915), 
Maclnnes-Yeh  (1921),  Melander  (1915),  Myers-Acree  (1913),  Neg- 
baur  (1891),  Nernst  (1888),  Planck  (1890),  Pleijl  (1916),  Prideaux 
(1914),  Reisenfeld  (1901),  Sackur  (1901),  Schwyzer  (1914),  Tower 
(1896),  Weyl  (1905). 


CHAPTER  XII 

Hydrogen  Electrodes  and  Electrode  Vessels 

For  the  most  part  the  base  of  a  hydrogen  electrode  is  simply  a 
piece  of  platinum  foil  or  wire.  If  wire  is  used  an  end  is  fused 
into  a  glass  tube  carrying  mercury  to  form  a  convenient  means 
of  making  contact  with  the  lead  of  the  potentiometer  circuit. 
The  wire  may  then  be  wound  upon  a  machine  screw  to  give  it  a 
neat  form.  If  foil  is  used  a  piece  about  1  sq.  cm.  is  first  welded 
to  a  short  piece  of  No.  30  B.  S.  gauge  platinum  wire  by  tapping 
the  two  smartly  with  the  flat  end  of  a  punch  while  they  are  laid 
upon  a  flat  hard  surface  in  the  white  heat  of  a  blast  lamp.  Next 
draw  off  a  glass  tube  to  a  thin,  blunt  point  and  break  away  the 
capillary  until  the  wire  will  enter.  Slip  the  wire  in  until  the  foil 
touches  the  glass.  Then,  holding  the  wire  with  foil  uppermost, 
rotate  the  tube  with  the  junction  in  the  tip  of  a  fine  flame.  Let 
the  glass  fuse  until  a  perfect  seal  is  made  and  a  little  of  the  glass 
fuses  to  the  edge  of  the  foil.  The  steps  are  illustrated  in  figure 
16.  It  is  important  to  avoid  a  seal  with  too  thin  a  glass  junc- 
tion, for  such  a  seal  will  easily  crack.     It  is  likewise  important 


Fig.  16.  Construction  of  Simple  Electrode 

to  avoid  too  heavy  a  junction  for  proper  annealing  then  becomes 
difficult.  To  anneal  hold  the  electrode  directly  after  its  construc- 
tion in  a  smoky  flame  and  gradually  remove  to  cooler  and  cooler 
parts  of  the  flame.  If  a  light  but  substantial  junction  is  made 
with  the  edge  of  the  foil  the  electrode  will  be  rugged. 

In  place  of  the  platinum  foil  gauze  is  sometimes  successfully 
used.  The  advantage  is  a  larger  surface;  but  gauze  will  make  a 
careful  technician  nervous  over  the  problem  of  thoroughly  clean- 
ing the  crevices. 

173 


174  THE   DETERMINATION   OF   HYDROGEN   IONS 

It  is  sometimes  assumed  that  complete  equilibrium  can  be  at- 
tained only  when  the  hydrogen  in  the  interior  of  the  metal  sup- 
porting the  platinum  black  is  in  equilibrium  with  that  on  the, 
surface.  To  reduce  the  time  factor  of  this  soaking-in  process  it 
is  considered  advantageous  to  use  as  the  supporting  metal  a  very 
thin  film  of  platinum  or  iridium  deposited  upon  glass.  Doubt- 
less the  finest  of  such  films  could  be  deposited  by  holding  the  glass 
tangent  to  the  Crookes'  dark  space  of  a  vacuum  discharge  and 
spattering  the  metal  on  from  electrodes  under  5000  volts  difference 
of  potential.  The  method  practiced  is  to  burn  the  metal  on  from  a 
volatile  solvent.  The  recipe  given  by  Westhaver(1905)  is  as  fol- 
lows: 0.3  gram  iridium  chloride  moistened  with  concentrated  HC1 
is  dissolved  in  1  cc.  absolute  alcohol  saturated  with  boric  acid. 
To  this  is  added  a  mixture  of  1  cc.  Venetian  turpentine  and  2  cc. 
lavender  oil.  The  glass  after  being  dipped  in  this  solution  is 
rotated  while  drying  to  give  an  even  deposit.  It  should  then  be 
very  carefully  dried  to  prevent  blistering  during  the  ignition. 
On  gradually  heating  over  an  alcohol  flame  there  is  at  last  produced 
a  very  thin  film  of  iridium.  The  process  should  be  repeated 
until  a  good  conducting  film  is  obtained. 

Gooch  and  Burdick  (1912)  have  better  success  with  a  viscous 
mixture  of  pure  chloroplatinic  acid  and  glycerine.  This  is  ap- 
plied with  an  asbestos  swab  to  the  glass  which  has  previously 
been  heated  to  a  temperature  which  will  instantly  volatilize  the 
glycerine.  The  resulting  film  is  heated  until  it  adheres  well 
to  the  glass. 

Meillere  (1920)  gives  the  following  recipe.  0.5  gram  dry 
platinum  chloride  is  triturated  with  10  or  15  grams  of  essence  of 
camomile.  The  mixture  is  thinned  with  about  an  equal  volume 
of  methyl  alcohol. 

If  after  some  practice  it  is  found  that  even  deposits  can  be 
formed  by  one  or  another  of  the  methods,  the  next  difficulty  met 
is  in  obtaining  good  adherence  of  the  film  to  the  glass.  This 
must  be  done  by  heating  sufficiently  but  at  the  same  time  there 
must  be  avoided  a  fusion  of  such  extent  that  the  continuity  of 
the  metallic  film  will  be  destroyed.  Such  a  fusion  will  be  more 
easily  avoided  and  at  the  same  time  volatilization  of  impurities 
in  the  film  will  be  made  easier  because  of  the  higher  temperature 


HYDROGEN   ELECTRODES  175 

permitted,  if  the  glass  support  is  made  of  a  "hard"  glass.  How- 
ever, in  the  selection  of  such  a  glass  one  with  a  temperature 
coefficient  of  expansion  approximately  equal  to  the  platinum 
should  be  selected, — chiefly  as  a  provision  for  the  next  step  which 
will  now  be  described. 

The  chief  technical  difficulty  in  the  preparation  of  electrodes 
with  the  films  described  is  in  establishing  the  necessary  electrical 
connection.  An  exposed  platinum  wire  contact  destroys  the 
object  in  using  the  film.  Ordinarily  the  electrode  is  made  by  first 
coating  a  bar  of  glass  in  the  end  of  which  there  is  sealed  a  plati- 
num wire  and  then  fusing  this  bar  into  the  end  of  a  glass  tube  so 
that  the  platinum  contact  is  exposed  within  the  tube  where 
mercury  contact  may  be  made.  Connection  with  the  film  is  made 
by  the  film  of  metal  that  runs  through  the  glass  seal.  It  is  less 
clumsy  to  seal  the  wire  into  the  end  of  a  glass  tube,  break  off 
the  wire  flush  with  the  glass,  coat  the  tube  with  the  film  and 
then  close  over  the  exposed  wire  with  a  drop  of  molten  glass. 

A  scheme  which  is  said  to  partially  accomplish  the  purpose 
of  a  thin  film  of  supporting  metal  is  to  cover  a  platinum  support 
with  a  gold-plate,  gold  being  relatively  impervious  to  hydrogen. 
It  is  doubtful  whether  this  reason  has  much  practical  weight. 
However  a  gold-plate  is  of  great  advantage.  If  offers  a  surface 
upon  which  deposits  of  "black"  adhere  well.  It  forms  a  support 
easily  dissolved  by  electrolysis  in  hydrochloric  acid,  thus  provid- 
ing an  easy  means  of  removing  old  deposits.  And  the  character 
of  the  gold  deposit  gives  an  additional  means  of  testing  the  clean- 
liness of  the  electrode  prior  to  blackening. 

For  the  gold  plating  of  electrodes  the  following  recipe  may  be 
used.  Dissolve  0.7  gram  gold  chloride  in  50  cc.  water  and  pre- 
cipitate the  gold  with  ammonia  water,  taking  care  to  avoid  an 
excess.  Filter,  wash  and  dissolve  immediately  in  a  KCN  solution 
consisting  of  1.25  grams  KCN  in  100  cc.  water.  Boil  till  the  solu- 
tion is  free  from  the  odor  of  ammonia. 

DEPOSITION  OF  "BLACK" 

According  to  the  work  of  earlier  investigators  and  the  con- 
sensus of  opinion  among  more  recent  investigators  there  seems  to 
be  no  difference  under  equilibrium  conditions  between  coatings  of 
platinum-,  iridium-  or  palladium-black.     No  recent  detailed  data 


176  THE    DETERMINATION    OF   HYDROGEN   IONS 

are  available  however.  Of  the  three,  iridium  is  recommended  by 
Lewis,  Brighton  and  Sebastian  because  of  its  higher  catalytic  ac- 
tivity, and  palladium  by  Clark  and  Lubs  (1916)  for  use  in  the 
study  of  physiological  solutions  because  of  the  relative  ease  with 
which  one  deposit  may  be  removed  before  the  deposition  of  the 
next  in  the  frequent  renewals  which  are  often  necessary.  Pal- 
ladium black  is  easily  removed  by  electrolysis  in  HC1.  Deposits 
of  platinum  or  iridium  may  be  removed  by  electrolysis  in  HC1 
solution,  if  they  are  deposited  upon  a  gold  plate. 

One  of  the  essentials  for  making  good  deposits  is  a  very  high 
degree  of  cleanliness  of  the  electrode.  •  A  good  test  is  the  evenness 
with  which  bubbles  of  hydrogen  escape  from  the  surface  during 
electrolysis.  Another  essential  in  the  preparation  of  a  good  elec- 
trode is  that  the  deposit  of  black  metal  be  not  only  even  but  of 
proper  thickness.  The  inclination  is  to  make  the  deposit  too 
thick,  with  the  production  of  a  sluggish  electrode.  To  obtain 
evenness  of  deposit  it  is  necessary  to  hold  down  the  dimensions 
of  the  electrode,  provide  more  than  one  lead,  or  modify  the  rate 
of  deposit.  With  this  much  said  there  remains  very  little  system- 
atized information  upon  the  composition  of  solutions  and  the 
current  densities  which  are  best  for  the  deposition  of  the  finely 
divided  metal  required. 

For  the  deposition  of  platinum  black  Ellis  (1916)  uses  a  solution 
of  pure  chloroplatinic  acid  containing  1  per  cent  Pt.  He  cau- 
tions against  the  use  of  the  lead  acetate  which  has  come  down  to 
us  in  recipes  for  the  deposition  of  platinum  black  upon  electrodes 
for  conductivity  measurements.  For  the  deposition  Ellis  uses  a 
small  auxiliary  electrode  and  a  current  large  enough  to  liberate 
gas  freely  at  both  electrodes.  He  continues  the  deposition  with 
five-minute  reversals  of  current  for  two  hours  and  obtains  a  very 
thick  coating.  The  author  prefers  an  adherent,  even,  thin  de- 
posit sufficient  to  just  cover  the  glint  of  metal  beneath.  In  com- 
parison of  one  against  another  in  the  same  solution  such  thin  de- 
posits are  found  to  agree  within  0.02  millivolt.  They  may  be 
deposited  within  a  minute  from  the  solutions  used  by  the  author. 

For  the  deposition  of  iridium  Lewis,  Brighton  and  Sebastian 
(1917)  make  the  gold  or  gold-plated  electrode  the  cathode  in  a 
5  per  cent  solution  of  iridium  chloride.  "The  best  results  were 
obtained  with  a  very  small  current  running  for  from  twelve  to 


HYDROGEN   ELECTRODES  177 

twenty-four  hours.  Too  large  a  current  gives  a  deposit  which 
appears  more  like  platinum  black  and  which  is  easily  rubbed  off. " 

The  author  has  used  deposits  of  platinum,  iridium  and  palla- 
dium upon  platinum,  upon  gold-plated  platinum  and  upon  "rho- 
tanium"  alloy.  Acidified  (HC1)  3  per  cent  solutions  of  the  chlorides 
of  each  metal  are  used  without  much  attention  to  the  exact 
strength.  The  current  from  a  four- volt  storage  battery  is  allowed 
to  produce  a  vigorous  evolution  of  gas.  The.  electrode  is  plunged, 
immediately  after  the  deposition,  into  a  dilute  sulfuric  acid  solu- 
tion and  electrolyzed.  It  is  required  that  the  bubbles  of  hydro- 
gen then  escaping  come  off  evenly,  that  the  electrode  be  evenly 
covered  with  the  deposit  in  thickness  sufficient  to  cover  the  glint 
of  polished  metal,  and  that  the  deposit  shall  adhere  under  a  vigor- 
ous stream  of  water.  No  electrode  is  ever  subjected  to  blast 
lamp  treatment  as  is  sometimes  recommended.  Instead,  renewals 
are  made  by  removing  the  old  deposit  by  electrolysis  in  HO 
solution,  and,  if  any  defect  whatsoever  develops  to  prevent  a 
good  redeposition  after  such  electrolysis,  the  electrode  is  retired 
from  duty. 

It  must  be  admitted  that  the  above  description  is  loose. 
This  is  because  the  rush  of  experimental  application  has  prevented 
a  detailed  examination  of  conditions,  and  experience  has  taught 
details  difficult  to  formulate  in  exact  language.  No  detailed 
descriptions  have  been  found  in  the  literature  and  those  that  are 
found  are  quite  inadequate  to  account  for  the  varied  deposits  some- 
times formed.  One  item  which  it  would  be  interesting  to  investi- 
gate is  the  influence  of  the  hydrogen  ion  concentration  of  the 
solution  upon  the  character  of  the  deposit.  Since  there  is  a 
simultaneous  deposit  of  metal  and  hydrogen  and,  since  the  char- 
acter of  the  platinum,  palladium  or  iridium  black  is  undoubtedly 
due  to  the  vigor  of  the  hydrogen  evolution,  it  is  evident  that  the 
pH  of  the  solution  constitutes  a -part  of  the  conditions. 

It  may  be  said  however,  that  ordinarily  there  is  little  difficulty 
in  obtaining  an  active  deposit  if  the  metal  concentration  is  main- 
tained as  the  solution  is  used,  if  electrodes  are  kept  thoroughly 
clean  and  if  the  solutions  are  kept  free  from  even  those  impurities 
which  collect  as  a  film  upon  exposed  solutions.  To  remove  these 
films  suck  them  off  with  a  clean  tube  attached  to  a  filter  pump. 

The  system  used  by  the  author  for  deposition  of  "black"  is 


178  THE   DETERMINATION   OF   HYDROGEN   IONS 

as  follows.  A  row  of  small  vessels,  such  as  weighing  bottles 
about  2  cm.  diameter  and  5  cm.  deep  are  fitted  with  electrodes. 
These  electrodes  are  all  attached  through  binding  posts  mounted 
on  a  wooden  rail.  These  in  turn  are  connected  to  one  pole  of 
a  double-pole,  double-throw  switch.  The  opposite  pole  is  con- 
nected with  a  flexible  lead  tipped  with  platinum.  This  lead  is 
used  to  connect  with  the  electrodes  to  be  treated.  Tl>e  middle 
connections  of  the  double-throw  switch  are  connected  with  a 
4-volt  storage  battery.  The  other  connections  are  cross-wired. 
One  of  the  vessels  is  filled  with  hydrochloric  acid  made  by  a 
one-to-one  dilution  of  ordinary  37  per  cent  acid.  This  is  used 
to  dissolve  previous  deposits  with  the  aid  of  electrolysis  (switch 
reversed,  treated  electrode  +)•  Another  vessel  is  filled  with  10 
per  cent  sulfuric  acid  for  preliminary  direct  and  counter-electrol- 
ysis in  testing  the  cleanliness  of  the  electrode.  Another  vessel 
is  filled  with  the  platinum,  palladium  or  iridium  chloride  solution. 
When  using  palladium  so-called  reagent  palladium  is  used  as  + 
electrode  and  this  is  removed  from  the  solution  when  not  in  use. 
After  deposition  of  the  black  the  electrode  under  treatment  is 
quickly  placed  under  a  vigorous  stream  of  water  and  then  elec- 
trolyzed  in  a  another  vessel  of  freshly  prepared  ten  per  cent  sul- 
furic acid  until  thoroughly  charged  with  hydrogen. 

When  used  with  inorganic  solutions  which  undergo  no  decom- 
position electrodes  may  often  be  used  repeatedly,  provided  they 
are  kept  clean  and  not  allowed  to  dry.  When  there  is  any  sign 
or  suspicion  of  an  electrode  becoming  clogged,  poisoned,  worn, 
dry  or  in  any  way  injured,  there  should  be  not  the  slightest  hesi- 
tation in  reblackening  or  even  rejecting  it.  It  is  therefore  not 
good  practice  to  so  tie  up  a  particular  electrode  with  an  expensive 
stopper  or  vessel  that  there  will  be  hesitation  in  rejecting  it. 

HYDROGEN   ELECTRODE    VESSELS 

So  many  types  of  vessel  have  been  published  that  it  is  diffi- 
cult to  do  justice  to  the  advantages  of  each.  The  selection  must 
depend  in  some  instances  upon  the  material  to  be  handled,  but  in 
any  case  there  are  a  few  principles  which  it  is  hoped  will  be  made 
clear  by  a  discussion  of  a  few  of  the  more  widely  used  vessels. 

The  general  method  of  operation  is  to  partially  or  wholly  im- 


HYDROGEN   ELECTRODES 


179 


merse  the  electrode  in  the  solution  to  be  measured  and  then  to 
bubble  hydrogen  through  the  vessel  till  constant  potential  is 
attained.  The  vessel  described  by  Lewis,  Brighton  and  Sebastian 
(1917)  and  illustrated  in  figure  17  is  representative  of  the  general 
type  of  vessel  used  for  what  may  be  called  the  classic  mode  of 
operation.     The  following  is  the  quoted  description  of  this  vessel : 


Fig.  17.  Hydrogen  Electrode  Vessel  of  Lewis,  Brighton  and 

Sebastian 

Hydrogen  from  the  generator  enters  at  A,  and  is  washed  in  the  bubbler 
B  with  the  same  solution  that  is  contained  in  the  electrode  vessel.  This 
efficient  bubbling  apparatus  saturates  the  gas  with  water  vapor,  so  that 
the  current  of  hydrogen  may  run  for  a  long  period  of  time  without  changing 
the  composition  of  the  solution  in  the  main  vessel.  The  gas  rises  from  the 
tip  C,  saturating  and  stirring  the  whole  liquid  from  G  to  F,  and  leaves  the 
apparatus  through  the  small  trap  E,  which  also  contains  a  small  amount 
of  the  same  solution.  The  platinum  wire  attached  to  the  electrode  D  is 
sealed  by  lead  glass  into  the  ground  glass  stopper  M.  L  is  a  joint  made  by 
fusing  together  the  end  of  the  platinum  wire  and  the  connecting  wire  of 
copper.  The  surface  of  the  solution  stands  at  the  height  F  so  that  the 
iridium  electrode  is  about  one-half  immersed.  The  apparatus  from  F 
through  G,  H,  I  to  J  is  filled  with  the  solution.  With  the  form  of  construc- 
tion shown  it  is  an  easy  matter  to  fill  the  tube  without  leaving  any  bubble? 


180  THE    DETERMINATION    OF   HYDROGEN   IONS 

of  air.  The  reservoir  K  filled  with  the  same  solution  serves  to  rinse  out 
the  tube  I,  J  from  time  to  time.  The  whole  apparatus  may  be  mounted 
upon  a  transite  board,  or  for  the  sake  of  greater  mobility,  may  be  held  in  a 
clamp,  the  several  parts  being  rigidly  attached  to  one  another  to  avoid 
accidental  breakage.  The  whole  is  immersed  in  the  thermostat  about  to 
the  point  L. 

The  tube  J  dips  into  an  open  tube  through  which  communication  is  made 
to  other  electrode  vessels.  This  connecting  tube  may  be  filled  with  the 
same  solution  as  is  contained  in  the  hydrogen  electrode  vessel  or  with  any 
other  solution  which  is  desired.  All  measurements  with  acids  are  made 
with  one  of  the  stopcocks  H,  I,  closed.  These  stopcocks  are  not  greased 
and  there  is  a  film  of  acid  in  the  closed  stopcock  which  suffices  to  carry  the 
current  during  measurement.  In  Order  to  make  sure  that  no  liquid  poten- 
tial is  accidentally  established,  the  second  stopcock  may  be  closed  up  and 
the  first  opened.  No  difference  of  potential  in  acid  solution  has  ever  been 
observed  during  this  procedure  (but  this  is  not  true  for  solutions  of  salt 
and  alkalies).  If  it  is  desired  that  both  stopcocks  be  open,  the  same 
liquid  that  is  in  the  electrode  vessel  is  placed  in  the  connecting  tube  at  J 
and  the  stopcocks  H  and  I  are  opened  after  the  current  of  hydrogen  has  been 
cut  off  by  the  stopcock  A,  and  the  opening  of  the  trap  E  has  been  closed. 

If  hydrogen  enters  the  cell  at  the  rate  of  one  or  two  bubbles  per  minute 
several  hours  are  required  for  the  saturation  of  the  solution  and  for  the 
removal  of  air.  After  this  time  the  potential  is  absolutely  independent  of 
the  rate  of  flow  of  hydrogen  and  the  generator  may  be  entirely  cut  off  for 
many  hours  without  any  change. 

For  some  biochemical  studies  such  a  vessel  is  unsuitable.  It 
is  sometimes  absolutely  essential  that  equilibrium  potentials  be 
established  rapidly.  The  necessity  is  perfectly  apparent  when  one 
is  dealing  with  an  actively  fermenting  culture.  It  is  not  always 
so  apparent  when  dealing  with  other  solutions,  but  it  is  suspected 
that  absolutely  complete  equilibrium  is  never  attained  in  some 
complex  biochemical  solutions  and  that  we  have  to  depend  upon 
speeding  up  the  reaction  between  hydrogen  and  hydrogen  ions  till 
a  virtual  equilibrium  point  is  attained  (see  Chapter  XVII) . 

It  was  shown  by  Michaelis  and  Rona  (1909)  that  a  fairly  con- 
stant E.  M.  F.  is  quickly  attained,  even  in  blood,  if  the  platinized 
electrode,  previously  saturated  with  hydrogen,  is  allowed  to  merely 
touch  the  surface  of  the  solution.  This  is  probably  due,  as  sug- 
gested by  Hasselbalch  (1913)  and  again  by  Konikoff  (1913),  to  a 
rather  sharply  localized  equilibrium  at  the  point  of  contact.  Re- 
ductions and  gas  interchanges  having  taken  place  within  the  small 
volume  at  the  point  of  contact,  diffusion  from  the  remaining  body 
of  the  solution  is  hindered  by  the  density  of  the  surface  layer 
with  which  alone  the  electrode  comes  in  contact. 


HYDROGEN    ELECTRODES  181 

In  exploring  new  fluids  it  appeared  hazardous  to  the  writer  to 
rely  upon  such  a  device,  which  appears  to  take  advantage  of  only 
a  localized  and  hence  a  pseudo-equilibrium,  and  which  makes  no 
allowance  for  a  possible  difference  between  the  solution  and  sur- 
face film  in  the  activity  of  the  hydrogen  ions.  Hasselbalch's 
(1911)  principle  seemed  therefore  to  be  more  suitable. 

Hasselbalch  found  that  a  very  rapid  attainment  of  a  constant 
potential  can  be  obtained  by  shaking  the  electrode  vessel.  Un- 
der these  conditions  there  should  be  not  only  a  more  rapid  inter- 
change of  gas  between  the  solution,  the  gaseous  hydrogen,  and 
the  electrode,  an  interchange  whose  rapidity  Dolezalek  (1899) 
and  Bose  (1900)  consider  necessary,  but  the  combined  or  molec- 
ular oxygen,  or  its  equivalent,  in  the  whole  solution  should 
be  more  rapidly  brought  into  contact  with  the  electrode  and  there 
reduced.  Furthermore,  by  periodically  exposing  the  electrode  the 
hydrogen  is  required  to  penetrate  only  a  thin  film  of  liquid  before 
it  is  absorbed  by  the  platinum  black.  The  electrode  should  there- 
fore act  more  rapidly  as  a  hydrogen  carrier.  For  these  reasons  a 
true  equilibrium  embracing  the  whole  solution  should  be  rapidly 
obtained  with  the  shaking  electrode;  and  indeed  a  constant 
potential  is  soon  reached. 

Eggert  (1914-1915)  in  Nernst's  laboratory  made  a  study  of  the 
rapidity  of  reduction  by  hydrogen  electrodes  in  which  he  com- 
pared the  effect  of  alternate  immersion  and  exposure  to  the  hydro- 
gen atmosphere  with  the  effect  of  continued  immersion.  In  the 
reduction  of  metal  salt  solutions  such  as  ferric  salts  he  obtained 
a  much  greater  velocity  of  reduction  when  the  electrode  was 
periodically  removed  from  the  liquid  carrying  a  thin  film  of  solu- 
tion to  be  exposed  to  the  hydrogen.  The  maximum  velocity 
was  proportional  to  the  platinum  surface  and  the  time  of  contact 
with  the  gas.  It  was  independent  of  the  number  of  times  per 
ninute  the  electrode  was  raised  and  lowered.  As  the  reaction 
leared  completion  the  decrease  in  velocity  of  reaction  became 
exponential. 

Making  use  of  the  principles  brought  out  in  the  preceding  dis- 
cission and  also  certain  suggestions  noted  in  the  chapter  on  liquid 
unction  potentials  Clark  (1915)  designed  a  vessel  which  appears 
o  have  found  favor  for  general  use.  A  working  drawing  of  this 
ressel  is  shown  in  figure  18.     If  solutions  more  viscous  than  fresh 


182 


THE   DETERMINATION    OF   HYDROGEN   IONS 


milk  are  to  be  used,  the  bores  of  the  inlet  and  outlet  tubes 
should  be  made  larger.  If  only  very  small  quantities  of  the  solu- 
tions to  be  tested  are  available,  the  dimensions  of  the  vessel 
may  be  reduced.  In  figure  19  is  a  diagrammatic  sketch  of  the 
complete  system  now  in  use  by  the  author  for  ordinary  work. 


(ron  no.  o  stopper) 


/eo° 


Fig.  18.  A  Hydrogen  Electrode  Vessel  (Clark,  1915) 

Notes.  In  submitting  this  working  drawing  to  a  glass  blower  it  shall  be 
specified  that:  (1)  Cocks  shall  be  joined  to  chamber  with  a  neat  and  wide 
flare  that  shall  not  trap  liquid.  (2)  Cocks  shall  be  ground  to  hold  high 
vacuum.  (3)  Bores  of  cock  keys  shall  meet  outlets  with  precision.  (4) 
The  handles  of  keys  shall  be  marked  with  colored  glass  to  show  positions  of 
bores.  (5)  The  handles  of  both  keys  shall  be  on  the  same  side  (front  of 
drawing).  (6)  Vessel  shall  be  carefully  annealed.  (7)  Opening  for  no.  0 
rubber  stopper  shall  be  smooth  and  shall  have  standard  taper  of  the  stand- 
ard no.  0  stopper.  (8)  Dimensions  as  given  shall  be  followed  as  closely  as 
possible.  (9)  No  chipped  keys  or  violation  of  the  above  specifications 
shall  be  accepted. 


HYDROGEN    ELECTRODES 


183 


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184         THE  DETERMINATION  OF  HYDROGEN  IONS 

The  electrode  vessel  is  mounted  in  a  clamp  pivoted  behind  the 
rubber  connection  between  J  and  H.  This  clamp  runs  in  a  groove 
of  the  eccentric  I,  the  rotation  of  which  rocks  the  vessel.  In  the 
manipulation  of  the  vessel,  the  purpose  is,  first,  to  bring  every 
portion  of  the  solution  into  intimate  contact  with  the  electrode 
F  and  the  hydrogen  atmosphere,  to  make  use  of  the  principle  of 
alternate  exposure  and  immersion  of  electrode  and  then,  when 
equilibrium  is  attained,  to  draw  the  solution  into  contact  with 
concentrated  KC1  solution  and  form  a  wide  contact  at  H  in  a 
reproducible  manner.  The  E.  M.  F.  is  measured  directly  after 
the  formation  of  this  liquid  junction. 

The  vessel  is  first  flooded  with  an  abundance  of  hydrogen  by 
filling  the  vessel  as  full  as  possible  with  water,  displacing  this 
with  the  hydrogen,  and  then  flushing  with  successive  charges  of 
hydrogen  from  the  backed-up  generator.  Water  or  solution  is 
run  into  the  vessel  from  the  reservoir  D  which  can  be  emptied 
through  the  drain  B  by  the  proper  turning  of  the  cock  C.  Solu- 
tion or  hydrogen  displaced  from  the  vessel  is  drained  off  at  B'. 
These  drains  when  they  leave  the  electrical  shielding  (see  p. 
231)  should  hang  free  of  any  laboratory  drain. 

With  the  vessel  rocked  back  to  its  lowest  position  the  solution 
to  be  tested  is  run  in  from  D  (after  a  preliminary  and  thorough 
rinsing  of  the  vessel  with  the  solution)  until  the  chamber  E  is  about 
half  full.  Cock  G  is  closed  and  cock  C  is  turned  so  as  to  permit  a 
constant  pressure  of  hydrogen  from  A  to  bear  upon  the  solution. 
For  very  careful  work  it  is  well  to  bubble  hydrogen  through  the 
solution.  The  rocking  is  then  commenced  and  is  continued  until 
experience  shows  that  equilibrium  is  attained  with  the  solution  of 
the  type  under  examination.  The  eccentric  I  should  give  the 
vessel  an  excursion  which  will  alternately  completely  immerse  the 
electrode  F  and  expose  it  all  to  the  hydrogen  atmosphere.  The 
rate  of  rocking  may  be  adjusted  to  obtain  the  maximum  mixing 
effect  without  churning. 

To  establish  the  liquid  junction  the  rubber  tube  between  J  and 
H  is  pinched  while  G  is  turned  to  allow  KC1  solution  to  escape  at 
B'.  Then  a  turn  of  G  and  the  release  of  the  pinch  draws  the  solu- 
tion down  through  the  cock  to  form  a  broad  mixed  junction  at  H. 
For  a  new  junction  the  old  is  flushed  away  with  fresh  KC1  from  the 
reservoir  N  by  properly  setting  cock  L. 


HYDROGEN    ELECTRODES  185 

With  the  closed  form  of  calomel  electrode,  M,  shown  in  the  figure 
no  closed  stopcocks  need  be  interposed  between  the  terminals  of 
the  chain.  With  the  customary  calomel  electrode  vessel  it  is 
necessary  to  use  a  closed  cock  somewhere  and  since  this  must  be 
left  ungreased  it  is  well  to  have  it  a  special  cock1  at  J. 

If  a  tube  be  led  out  from  J  and  branched,  several  hydrogen 
electrode  vessels  may  be  joined  into  the  system.  At  all  events  it 
is  well  to  work  with  two  vessels  in  parallel  so  that  one  may  be 
flushing  with  hydrogen  while  the  other  is  shaking. 

The  electrode  F  is  supported  in  a  sulfur-free  rubber  stopper. 
A  glass  stopper  may  be  ground  into  place  but  is  seldom  of  any 
advantage  and  may  prove  to  be  a  mistake.  In  the  first  place  it 
is  advisable  to  be  free  with  electrodes  and  to  instantly  reject  any 
which  fail  to  receive  a  proper  coating  of  metal.  The  inclination  to 
do  this  is  less  if  it  entails  the  rejection  of  a  carefully  ground  stop- 
per. Unless  the  stopper  is  accurately  ground  into  place  it  is 
worthless.  Furthermore  it  is  very  difficult  to  so  grind  a  glass 
stopper  that  there  will  be  left  no  capillary  space  to  trap  liquid.  A 
rubber  stopper  can  be  forced  into  place  without  leaving  such  a 
space.  The  rapidity  with  which  measurements  are  usually  taken 
makes  it  improbable  that  a  rubber  stopper,  if  made  sulfur  free, 
can  have  any  appreciable  effect.  If  the  rubber  must  be  pro- 
tected a  coating  of  paraffine  will  do. 

The  calomel  electrode  M  is  of  the  saturated  type  so  that  no 
particular  care  need  be  taken  to  protect  it  from  the  saturated  KC1 
used  in  making  junctions.  This  is  the  working  standard  for  the 
accurate  standardization  of  which  there  is  held  in  reserve  the 
battery  of  accurately  made,  tenth-normal,  calomel  electrodes  P. 
This  battery  may  be  connected  with  the  system  at  any  time  by 
making  liquid  connection  at  0  and  opening  K.  After  a  measure- 
ment the  liquid  junction  is  eliminated,  the  space  rinsed  with  the 
tenth  normal  KC1,  and  liquid  contact  left  broken. 

The  design  of  this  system  is  obviously  for  an  air  bath.  The 
necessity  of  raising  cocks  out  of  an  oil  bath  would  not  permit 
such  direct  connections  as  are  here  shown. 

1  To  make  an  easily  turning  cock  out  of  which  KC1  will  not  creep,  grease 
the  narrow  part  of  the  socket  and  the  wide  part  of  the  key.  When  the  key 
is  replaced  there  will  be  two  bands  of  lubricant  on  which  the  key  will  ride 
with  an  uncontaminated  zone  between  for  the  film  of  KC1  solution. 


186         THE  DETERMINATION  OF  HYDROGEN  IONS 


Fig.  20.  Types  of  Hydrogen  Electrode  Vessels 

\ 


HYDROGEN   ELECTRODES  187 

In  figure  20  are  shown  several  other  designs  of  electrode  vessels. 
A  is  one  of  the  original  Hasselbalch  vessels  which  have  since  been 
modified  for  the  use  of  replaceable  electrodes.  B  (S0rensen),  (Ellis) 
and  C  (Walpole),  are  operated  in  a  manner  similar  to  the  vessel 
shown  in  figure  18.  Walpole 's  vessel  was  made  of  silica  and  the 
electrode  was  of  platinum  film  as  described  on  page  174.  D  (Mc- 
Clendon  and  Magoon)  was  designed  for  determinations  with  small 
quantities  of  blood.  E  (Michaelis) ,  employs  a  stationary  hydrogen 
atmosphere  and  a  wick  connection  for  the  liquid  junction.  G  (Long) 
is  a  simple  device  which  the  designer  thought  applied  the  essential 
principles  of  Clark's  vessel.  Barendrecht  's  vessel,  H,  is  designed  for 
immersion  in  an  open  beaker  for  estimations  during  titrations. 
It  is  similar  to  a  design  of  Walpole 's  (1914),  but  is  provided  with 
a  plunger  the  working  of  which  permits  the  rinsing  of  the  bulb  and 
the  precise  adjustment  of  the  level  of  the  liquid.  Another  immer- 
sion electrode  is  Hildebrand's,  F,  the  successful  operation  of  which 
depends  upon  a  vigorous  stream  of  hydrogen,  which,  on  escaping 
from  the  bell  surges  the  solution  about  the  electrode.  A  modifi- 
cation which  provides  better  protection  of  the  electrode  from 
oxygen  is  Bunker's  design,  I. 

At  this  point  it  may  be  of  interest  to  note  that  Wilke  (1913)  at- 
tempted to  make  a  hydrogen  electrode  by  using  a  thin  tube  of  pal- 
ladium on  the  interior  of  which  hydrogen  was  maintained  under 
pressure.  One  of  the  difficulties  with  such  an  electrode  is  the 
estimation  of  the  hydrogen  pressure  at  the  solution-electrode  in- 
terface. Wilke 's  idea  has  never  been  developed  to  a  practical 
point  so  far  as  we  know,  but  it  is  worthy  of  study  as  an  im- 
mersion electrode  for  industrial  use. 

For  titrations  where  exact  control  of  liquid  junction  potential 
differences  is  of  relatively  less  importance  than  control  of  wastage 
of  the  material  titrated,  the  system  illustrated  in  figure  21  is 
useful.  Titrations  are  carried  on  in  the  Erlenmeyer  flask 
which  is  held  in  place  by  the  plate  P.  The  arm  carrying  the 
spring  may  be  attached  to  the  support  at  A  in  a  variety  of  ways. 
It  may  be  bolted,  riveted  or  screwed;  but  should  be  made  with 
a  "running  fit"  so  that  while  held  firmly,  it  may  be  turned  to 
permit  removal  of  the  Erlenmeyer.  The  plate  F  should  be  rigidly 
attached  to  the  support  at  B.  In  this  plate  there  is  turned  a 
hole  tapered  to  receive  snugly  the  rubber  stopper  which  holds 


188 


THE    DETERMINATION    OF   HYDROGEN    IONS 


the  various  attachments.     If  this  hole  is  left  rough  from  the  lathe 


tne  various  attachments.     11  tms  noie  is  leit  rough  trom  the  lathe 
tool  the  stopper  will  be  held  very  firmly  after  the  various  glass 


Fig  21.  A  Hydrogen  Electrode  Vessel  Suitable  for  Titrations 

tubes  have  been  forced  into  place.  '  The  support  has  been  illus- 
trated* in  the  drawing  as  if  it  were  at  the  left.  As  a  matter  of  fact 
it  is  behind  the  vessel,  and  carries  at  E  a  bar  which  supports  the 


HYDROGEN    ELECTRODES  189 

calomel  cell  K.  The  supporting  system  is  illustrated  roughly  for 
there  are  various  constructions  which  may  be  used.  In  the 
author's  apparatus  A  is  a  screw  connection  and  the  junctions  at  B 
and  E  are  riveted  and  soldered. 

It  is  of  course  essential  that  the  solution  be  shaken  after  each 
step  of  the  titration.  If  the  support  is  clamped  to  a  somewhat 
flexible  rod  the  whole  system  may  be  shaken.  Otherwise  the 
glass  vessel  should  be  protected  from  the  metal  of  the  supporting 
plate  by  an  inset  of  asbestos  wood  and  then,  if  the  spring  is  not 
too  stiff,  the  vessel  alone  may  be  swirled.  During  a  titration 
cock  M  is  kept  closed  and  N  is  left  open.  If  the  system  is  suffi- 
ciently rigid,  if  care  is  used  in  the  operation  of  the  cocks  and  if 
serious  temperature  changes  are  avoided  very  little  of  the  solu- 
tion will  be  drawn  into  the  capillary  S  and  very  little  of  the  KC1 
will  run  or  diffuse  into  the  solution. 

A  wire  form  of  electrode  will  withstand  shaking  and  possible 
scraping  better  than  a  foil  electrode. 

Hydrogen  is  delivered  beneath  the  surface  of  the  liquid.  At 
the  first  flushing  an  abundance  of  hydrogen  is  used;  later  but  little 
is  necessary.  The  hydrogen  escapes  through  a  tube  not  shown  and 
should  be  run  through  a  trap  having  a  shallow  layer  of  water. 

The  burette  tip  shown  in  the  figure  is  lengthened  by  a  piece 
of  capillary  tubing. 

If  the  hydrogen  be  replaced  by  purified  nitrogen  and  if  the 
platinized  electrode  be  replaced  by  a  gold-plated  electrode  this 
vessel  does  very  well  for  oxidation-reduction  titrations.  In  this 
case  the  nitrogen  is  delivered  above  the  solution  and  not  below  the 
surface. 

In  some  cases  a  preliminary  reduction  of  a  solution  may  be 
accomplished  by  making  the  solution,  in  the  presence  of  hydrogen, 
travel  down  a  long  spiral  of  platinized  wire.  The  spiral  is  made 
by  winding  no.  24  copper  wire  closely  upon  a  rod,  mounting  it 
with  a  spread  of  the  turns  just  sufficient  to  hold  together  descend- 
ing drops,  plating  with  gold  and  then  platinizing.  Liquid  de- 
livered slowly  at  the  top  of  the  spiral  will  be  broken  into  drops 
which  in  the  descent  of  the  spiral  are  thoroughly  stirred.  The 
reduced  solution  is  brought  into  contact  with  an  electrode  in  a 
constricted  part  of  the  enclosing  tube  and  is  then  delivere'd  to  a 
continuous-flow  liquid  junction  such  as  that  described  by  Lamb 


190         THE  DETERMINATION  OF  HYDROGEN  IONS 

and  Larson  or  Maclnnes  (see  page  168).  The  hydrogen  by  suit- 
able devices  may  be  given  the  carbon-dioxid  partial  pressure  of 
the  tested  solution.  Such  a  scheme  is  useful  only  in  dealing  with 
continuous  treatment  processes  where  abundance  of  material 
is  available. 

Keller  (1922)  has  described  a  hydrogen  electrode  with  a  re- 
placeable disk  of  platinum  gauze.  This  is  held  by  a  cap  to  a  hard 
rubber  support  which  contains  a  portable  calomel  electrode.  The 
system  is  rugged  and  may  be  used  as  an  immersion  chain  for 
determining  the  pH  values  of  liquids  in  commercial  processes. 

In  conclusion  it  may  be  said  that  with  ordinary  care  almost  any 
simple  combination  of  electrode  and  electrode  vessel  will  give 
fairly  good  results.  On  the  other  hand  it  is  often  necessary  not 
only  to  provide  against  continuous  loss  of  CO2  from  biological 
solutions  but  also  to  arrange  for  rapid  attainment  of  equilibrium. 
Since  electrode  measurements  are  often  the  last  resort,  since  one 
can  easily  be  misled  by  pseudo-equilibria  and  since  attention  to  a 
few  simple  details  of  construction  and  operation  frequently  in- 
creases very  greatly  the  speed  of  experimentation,  the  "simplicity" 
of  certain  designs  is  sometimes  more  apparent  than  real. 

However  it  would  be  invidious  to  select  any  particular  design 
for  criticism,  the  more  so  because  none  yet  published  is  perfectly 
adapted  to  all  purposes.  Those  described  are  therefore  to  be 
considered  as  illustrations  from  which  the  reader  may  select  items 
or  suggestions  to  incorporate  in  his  own  design. 

SUPPLEMENTARY  REFERENCES 

Bailey  (1920),  Baker-Van  Slyke  (1918),  Barendrecht  (1915),  Bose  (1900), 
Bunker  (1920),  Dolezalek  (1899),  Eggert  (1914-1915),  Ellis  (1916), 
Gooch-Burdick  (1912),  Clark  (1915),  Cullen  (1922),  Hasselbalch 
(1910-1913),  Hastings  (1921),  Hildebrand  (1913),  Hudig-Sturm  (1919), 
Konikoff  (1913),  Lewis-Brighton-Sebastian  (1917),  Linhart  (1919), 
Long  (,1916),  Loomis-Acree  (1911),  Maloney  (1921),  McClendon  (1915, 
1916,  1918),  McClendon-Magoon  (1916),  Michaelis  (1910, 1911, 1914), 
Michaelis-Rona  (1909),  Myers-Acree  (1913),  Peters  (1914),  Rudnick 
(1921),  Sand-Law  (1911),  S0rensen  (1909),  Sturm  (1918),  Treadwell- 
Weiss  (1920),  Walpole   (1913,  1914),  Westhaver  (1905),  Wilke  (1913). 


CHAPTER   XIII 
Calomel  Electrodes 

Unless  otherwise  specified  the  calomel  electrode  is  an  electrode 
in  which  mercury  and  calomel  are  overlaid  with  a  definite  concen- 
tration of  'potassium  chloride.  For  particular  purposes  HC1  calo- 
mel electrodes  or  those  containing  some  other  chloride  are  used. 

The  general  type  of  construction  is  shown  by  A,  fig.  23.  A  layer 
of  very  pure  mercury  is  covered  with  a  lajer  of  very  pure  calomel 
and  over  all  is  a  solution  of  a  definite  concentration  of  KC1  satu- 
rated with  calomel. 

The  difference  of  potential  between  mercury  and  solution  is 
determined  primarily  by  the  concentration  of  the  mercurous  ions 
supplied  from  the  calomel.  But,  since  there  is  equilibrium  be- 
tween the  calomel,  the  mercurous  ions  and  the  chlorine  ions,  the 
concentration  of  the  mercurous  ions  is  determined  by  the  chlorine 
ion  content  furnished  chiefly  by  the  KC1.  One  of  three  concentra- 
tions of  KC1  is  usually  employed — either  0.1  molecular,  1.0  molecu- 
lar or  saturated  KC1.  These  are  ordinarily  referred  to  as  the 
"tenth  normal-,"  "normal-"  or  "saturated  calomel  electrodes." 

The  mercury  used  in  the  preparation  of  these  electrodes  or 
"half-cells"  should  be  the  purest  obtainable.  In  Chapter  XV 
methods  of  purification  are  described.  Sufficient  mercury  should 
be  used  to  cover  the  platinum  contact  deeply  enough  to  prevent 
solution  reaching  this  contact  on  accidental  shaking. 

More  portable  half-cells  are  made  by  amalgamating  a  plati- 
num wire  or  foil.  This  is  done  by  electrolyzing  a  solution  of 
nercurous  nitrate,  the  wire  being  the  negative  pole.  Provision 
s  then  made  for  keeping  a  paste  of  calomel  about  this  wire. 

Some  success  has  been  attained  with  the  use  of  the  better 
grades  of  calomel  supplied  on  the  market  but  the  risk  is  so  great 
hat  it  is  best  to  prepare  this  material  in  the  laboratory.  A 
shemical  and  an  electrolytic  method  will  be  described. 

The  chemical  'preparation  of  calomel.  Carefully  redistill  the  best 
•btainable  grade  of  nitric  acid.  Dilute  this  slightly  and  with  it 
lissolve  some  of  the  mercury  prepared  as  described  in  Chapter 

191 


192  THE   DETERMINATION   OF   HYDROGEN    IONS 

XV,  always  maintaining  a  large  excess  of  mercury.  Throw  the 
solution  into  a  large  amount  of  distilled  water  making  sure  that 
the  resulting  solution  is  distinctly  acid.  Now,  having  distilled 
pure  hydrochloric  acid  from  a  20  per  cent  solution  and  taken  the 
middle  portion  of  the  distillate,  dilute  and  add  it  slowly  to  the 
mercurous  nitrate  solution  with  constant  stirring.  When  the 
precipitate  has  collected,  decant  and  treat  with  repeated  quanti- 
ties of  pure  distilled  water  (preferably  conductivity  water).  The 
calomel  is  sometimes  washed,  with  suction  upon  a  Buchner  funnel 
but  if  due  regard  be  taken  for  the  inefficiency  of  washing  by  de- 
cantation  it  is  preferable  to  wash  repeatedly  by  decantation  since 
there  is  thereby  obtained  a  more  even-grained  calomel.  Through- 
out the  process  there  should  be  present  some  free  mercury. 

Electrolytic  preparation  of  calomel.  Doubtless  the  better  prepa- 
ration of  calomel  is  formed  by  electrolysis  according  to  the  method 
of  Lipscomb  and  Hulett  (1916),  This  is  carried  out  in  the  same 
way  that  the  mercurous  sulfate  for  Weston  cells  is  formed.  For 
the  preparation  of  mercurous  sulfate  Wolff  and  Waters  (1907) 
employ  the  apparatus  shown  in  figure  22.  An  improvised  appa- 
ratus may  be  made  of  a  glass  tube  with  paddles,  platinum  wire 
electrode  and  mercury  contact  and  with  two  spools  for  bearing 
and  pulley.  In  place  of  the  sulfuric  acid  there  is  used  normal 
hydrochloric  acid.  A  direct  current  (from  a  four-volt  storage 
battery)  must  be  used.  The  alternating  current  sometimes  used 
in  the  preparation  of  mercurous  sulfate  does  not  seem  to  work  in 
the  preparation  of  calomel  according  to  some*  preliminary  experi- 
ments which  Mr.  McKelvy  and  Mr.  Shoemaker  of  the  Bureau  of 
Standards  kindly  made  for  the  writer.  During  the  electrolysis  the 
calomel  formed  at  the  mercury  surface  should  be  scraped  off  by 
the  paddles  c  and  c  (fig.  22).  The  calomel  formed  by  this  process 
is  heavily  laden  with  finely  divided  mercury. 

Calomel  formed  by  either  the  chemical  or  the  electrolytic  proc- 
ess should  be  shaken  with  repeated  changes  of  the  KC1  solution 
to  be  used  in  the  half -cell  before  the  calomel  is  placed  in  such  a 
cell. 

The  variations  in  the  potentials  of  calomel  electrodes  have  been 
the  subject  of  numerous  investigations.  Richards  (1897)  ascribed 
it  partly  to  the  formation  of  mercuric  chloride.  Compare  Rich- 
ards and  Archibald  (1902).     Sauer  (1904)  on  the  other  hand  con- 


CALOMEL   ELECTRODES 


193 


eluded  that  this  had  little  to  do  with  the  inconstancy.  Arguing 
upon  the  well  known  fact  that  the  solubility  of  slightly  soluble 
material  is  influenced  by  the  size  of  the  grains  in  the  solid  phase, 
Sauer  thought  to  try  the  effect  of  varying  the  grain  size  of  the  calo- 
mel as  well  as  the  effect  of  the  presence  of  finely  divided  mercury. 


Fig.  22.  Wolff  and  Waters'   Apparatus  for  the  Electrolytic 
Preparation  of  Mercurous  Sulfate  or  of  Calomel 

With  cells  made  up  with  various  combinations  he  found  the  fol- 
lowing comparisons : 


Hg-     calomel 

against 

calomel 

Hg+       = 

-  0.00287  volt 

(fine)     (coarse) 

(fine) 

(coarse) 

Hg~     calomel 

against 

calomel 

Hg+      = 

-  0.00037  volt 

(fine)     (coarse) 

(coarse) 

(coarse) 

Hg-     calomel 

against 

calomel 

Hg+      - 

-  0.0025  volt 

(coarse)  (coarse) 

(fine) 

(coarse) 

194 


THE  DETERMINATION  OF  HYDROGEN  IONS 


Fig.  23.  Types  of  Calomel  Electrode  Vessels 


CALOMEL   ELECTRODES  195 

Lewis  and  Sargent  (1909)  state  that  they  do  not  confirm  Sauer 
in  regard  to  the  effect  of  the  finely  divided  mercury  but  that  they 
do  confirm  him  in  regard  to  the  state  of  the  calomel.  These  au- 
thors and  others  recommend  that  grinding  the  calomel  with  mer- 
cury to  form  a  paste  be  avoided  as  this  tends  to  make  an  uneven 
grain.  It  is  better  to  shake  the  mercury  and  the  calomel  together 
but  this  is  unnecessary  if  electrolytic  calomel  is  used. 

Here  and  there  in  the  literature  we  find  various  other  sugges- 
tions such  as  the  elimination  of  oxygen  from  the  cell ;  but  there 
seems  to  be  no  very  substantial  agreement  in  regard  to  this  and 
several  other  matters  as  there  is  no  substantial  agreement  in  the 
preference  of  one  concentration  of  KC1  over  another.  By  the  use 
of  carefully  prepared  material  and  the  selection  of  the  better  agree- 
ing members  of  a  series,  calomel  electrodes  may  be  reproduced  to 
agree  within  0.1  millivolt  or  better;  but  it  has  not  yet  been  estab- 
lished whether  or  not  this  represents  the  order  of  agreement  among 
electrodes  made  in  different  laboratories.  Furthermore  there 
still  remains  the  question  of  the  effect  of  minor  disturbances. 
There  is  no  question  that  "true"  values  are  not  to  be  expected 
until  all  parts  of  the  system  are  in  equilibrium  and  that  a  prelimin- 
ary shaking  such  as  Ellis  uses  will  hasten  the  attainment  of  equilib- 
rium. On  the  other  hand  a  disturbance  which  will  alter  the 
surface  structure  of  the  mercury  exposed  may  produce  a  slight 
temporary  shift  in  the  potential  difference.  The  subject  remains 
'or  systematic  investigation. 

The  most  extensive  investigation  of  unsaturated  calomel  elec- 

rodes  was  made  by  Acree  and  his  students  (Myers  and  Acree, 

joomis  and  Acree),  but  how  far  the  reproducibility  which  they 

ittained  by  short  circuiting  the  differences  of  potential  is  repre- 

:  entative  of  the  general  reproducibility  of  such  electrodes  is  not 

;  ret  established. 

In  figure  23  are  shown  several  calomel  electrode  vessels  each 
'  rith  a  feature  that  may  be  adapted  to  a  particular  requirement. 
Valpole's  (1914)  vessel,  A,  is  providedwith  a  contact  that  leads 
<  ut  of  the  thermostat  liquid  and  with  a  three-way  cock  for  flushing 
i  way  contaminated  KC1.  A  more  elaborate  provision  for  the 
]  rotection  of  the  KC1  of  the  electrode  is  shown  in  the  vessel  of 
1  -ewis,  Brighton  and  Sebastian  (1917),  B.  A  form  useful  as  a  sat- 
i  rated  calomel  electrode  in  titrations  is  shown  at  C.     Fresh  KC1 


196  THE   DETERMINATION    OF   HYDROGEN    IONS 

passes  through  the  U-tube  to  take  the  temperature  of  the  bath 
and  to  become  saturated  with  calomel  shown  at  the  bottom  of 
this  U-tube.  D  is  Ellis'  (1916)  vessel,  which  in  the  particular 
form  shown  was  designed  to  be  sealed  directly  to  the  remainder  of 
the  apparatus  used.  A  valuable  feature  is  the  manner  of  making 
electrical  contact.  Instead  of  the  customary  sealed-in  platinum 
wire  Ellis  uses  a  mercury  column.  On  closing  the  cocks  the  ves- 
sel may  be  shaken  thoroughly  to  establish  equihbrium.  This 
feature  has  not  been  generally  practiced.  Vessel  E  is  a  simple 
form  useful  for  the  occasional  comparison  electrode.  It  may  be 
made  by  sealing  the  cock  of  an  ordinary  absorption  tube  to  a 
test  tube  and  adding  the  side  arm.  F  is  the  vessel  of  Fales  and 
Vosburgh  (1918)  with  electric  contact  made  as  in  the  familiar 
Ostwald  vessel  (G). 

In  adding  new  KC1  solution  to  a  vessel  it  must  be  borne  in  mind 
that  the  solution  should  be  saturated  with  calomel  before  equihb- 
rium can  be  expected.  It  is  well  therefore  to  have  in  reserve  a 
quantity  of  carefully  prepared  solution  saturated  with  calomel. 

Lewis,  Brighton  and  Sebastian  (1917)  state  that  certain  grades 
of  commercial  KC1  are  pure  enough  to  be  used  in  the  preparation 
of  KC1  solutions  for  the  calomel  electrode  while  other  samples 
"contain  an  unknown  impurity  which  has  a  surprisingly  large 
effect  upon  the  E.  M.  F.  and  which  can  only  be  eliminated  by 
several  recrystallizations. "  It  is  therefore  obvious  that  the  only 
safe  procedure,  in  lieu  Of  careful  testing  by  actual  construction  of 
electrodes  from  different  material,  is  to  put  the  best  available  KC1 
through  several  recrystallizations. 

Acree  has  called  attention  to  the  possible  concentration  of  the 
KC1  solution  by  the  evaporation  of  water  and  its  condensation  on 
the  walls  of  vessels  unequally  heated  in  thermostats. 

The  values  assigned  to  the  potential  differences  at  the  several 
calomel  electrodes  at  different  temperatures  vary.  A  judicious 
selection  will  wait  upon  the  consideration  of  several  important 
matters.  Some  of  the  more  important  of  these  will  be  presented 
in  Chapter  XIX.  At  this  point  however  we  may  recount  with- 
out comment  some  of  the  more  frequently  used  values  which  the 
reader  may  choose  to  use. 

Clark  and  Lubs  (1916)  give  the  following  compilation  of  Bjer- 
rum's  values  and  those  of  S0rensen  and  Koefoed  published  by 
S0rensen  (1912): 


CALOMEL   ELECTRODES 


197 


TABLE  42 


Bjerrum 

S0rensen  and  Koefoed 
Bjerrum 


S0rensen  and  Koefoed. 


TEMPERATURE 


°c. 
0 

18 
20 

25 

30 
40 
50 
60 
75 


POTENTIAL  DIFFERENCE  BE- 
TWEEN   NORMAL  HYDROGEN 
ELECTRODE    AND  N/10  CALOMEL 
ELECTRODE  WHEN  HYDROGEN 
PRESSURE  IS 


Oneatmosphere 

less  vapor 

pressure 


volts 

0.3366 

0.3377 
0.3375 

0.3367 

0.3364 
0.3349 
0.3326 
0.3290 
03243 


One 

atmosphere 


volts 

0.3367 

0.3380 
0.3378 

0.3371 

0.3370 
0.3359 
0.3344 
0.3321 
0.3315 


In  the  report  of  the  "Potential  Commission"  of  the  Bunsen- 
Gesellschaft  (Abegg,  Auerbach  and  Luther,  1911)  the  normal  hy- 
drogen electrode  standard  of  difference  of  potential  was  adopted. 
This  of  course  is  only  incidental  except  as  temperature  coefficients 
enter.  The  differences  of  potential  between  the  normal  hydrogen 
electrode  and  the  tenth-normal  and  normal  KC1  calomel  electrodes 
were  given  as  0.337  and  0.284-0.283  respectively.  .Auerbach 
(1912)  in  a  review  of  this  report  called  attention  to  the  smaller 
temperature  coefficient  of  the  potential  difference  at  the  tenth- 
normal calomel  electrode  when  referred  to  the  normal  hydrogen 
electrode  (as  having  zero  potential  difference  at  all  temperatures) 
and  suggested  that  the  tenth-normal  electrode  be  taken  as  the 
working  standard  with  the  value  0.3370  between  20°C.  and  30°C. 

Loomis  and  Acree  (1911)  present  a  choice  of  values  for  the 
tenth-normal  calomel  electrode  at  25°C.  referred  to  the  normal 
hydrogen  electrode.  The  choice  depends  upon  the  ionization  as- 
cribed to  the  hydrochloric  acid  solutions  used  in  their  hydrogen 
electrodes  and  upon  the  values  of  the  contact  differences  of  poten- 
tial which  were  involved.  Loomis  (1915)  i?  inclined  to  accept  the 
/alue  0.3360. 


198  THE   DETERMINATION   OF   HYDROGEN    IONS 

In  1914  Lewis  and  Randall  applied  "  corrected  degrees  of  dis- 
sociation" to  the  hydrochloric  acid  solutions  used  in  arriving  at 
the  difference  of  potential  at  25°  between  calomel  electrodes  and 
the  theoretical  normal  hydrogen  electrode.  Denning  the  normal 
calomel  electrode  as  the  combination  Hg  Hg2Cl2,  KC1  (1M),  KC1 
(0.1  M)  they  reach  the  value  0.2776.  The  difference  of  potential 
between  this  electrode  and  the  tenth  normal  they  give  as  0.0530. 
Whence  the  value  for  the  tenth  normal  electrode  is  0.3306.  These 
values  were  revised  by  Lewis,  Brighton  and  Sebastian  (1917) 
to  0.2828  for  the  difference  of  potential  between  the  normal 
calomel  and  the  normal  hydrogen  electrode,  and  0.0529  for  the 
difference  between  the  normal  and  the  tenth  normal. 

Beattie  (1920)  using  more  recent  data  calculates  for  the  poten- 
tial difference  at  the  normal  calomel  electrode  0.2826  and  com- 
pares this  value  with  0.2824  which  is  Lewis,  Brighton  and  Se- 
bastian's result  (see  above)  when  corrected  by  Beattie  for  the 
liquid  junction  potential  difference  between  0.1  N  and  1  N  KC1. 

It  will  have  been  noted  that  in  measurements  with  the  hydro- 
gen electrode  there  is  no  concern  for  the  absolute  difference  of 
potential  between  mercury  and  solution.  This  is  because  the  calo- 
mel half-cell  is  merely  a  convenient  go-between  for  measurements 
in  which  one  hydrogen  electrode  is  compared  with  another.  For 
this  reason  it  is  convenient  to  retain  the  "normal  hydrogen  elec- 
trode" standard  of  reference  and  it  so  happens  that  this  is  in 
harmony  with  a  general  though  not  universal  custom  adopted 
for  all  electrode  measurements. 

Other  systems  are:  first,  that  in  which  the  difference  of  poten- 
tial between  the  mercury  and  a  normal  concentration  of  KC1  in 
a  calomel  electrode  is  taken  arbitrarily  as  zero,  and  second  that 
in  which  this  difference  of  potential  is  given  what  is  considered 
to  be  its  actual  value. 

Largely  upon  the  basis  of  Palmaer's  (1903)  work  the  value  0.560 
volt  has  been  used  as  the  "absolute"  difference  of  potential 
between  mercury  and  N/1  KC1  saturated  with  calomel  in  the 
presence  of  solid  calomel  at  18°C.  (The  mercury  being  positive 
to  the  solution.)     There  is  some  skepticism1  regarding  the  re- 

1  Whether  this  is  just  or  unjust  is  a  question  concerning  which  we 
are  in  doubt.  No  critical  review  in  the  light  of  modern  researches  is  known 
to  the  author. 


CALOMEL   ELECTRODES  199 

liability  of  this  value,  but  for  the  particular  purpose  with  which 
we  are  now  concerned  it  makes  little  difference  what  the  value 
is  if  proper  relative  relations  are  maintained.  But  the  difficulty 
in  maintaining  proper  relative  relations  when  there  is  no  agree- 
ment on  a  standard  basis  of  reference  is  made  evident  when  we 
consider  that  the  temperature  coefficient  for  the  absolute  differ- 
ence of  potential  between  mercury  and  solution  is  very  different 
from  the  temperature  coefficient  for  the  difference  of  potential 
between  calomel  electrode  and  hydrogen  electrode  when  the 
normal  hydrogen  electrode  is  defined  as  having  zero  potential 
difference  at  all  temperatures.  Thus,  as  shown  by  Fales  and 
Mudge  (1920),  the  absolute  temperature  coefficient  of  the  satur- 
ated calomel  half-cell  is  low  and  has  a  positive  value.  But  the 
temperature  coefficient  of  the  values  for  the  saturated  calomel 
half-cell  as  used  in  hydrogen  electrode  work  is  negative  and 
high.  Fales  and  Mudge  seem  not  to  have  made  any  independent 
measurements  which  furnish  more  reliable  values  for  the  differ- 
ence of  potential  between  a  saturated  calomel  half-cell  and  the 
"normal  hydrogen  electrode."  These  authors  have  however 
extended  the  work  of  Michaelis  and  have  found  evidence  that 
the  saturated  calomel  half-cell  is  reliable  within  the  temperature 
interval  5°-60°C. 

As  a  working  standard  the  saturated  calomel  half-cell  is  un- 
doubtedly the  best  as  pointed  out  by  Michaelis  and  Davidsohn 
(1912).  It  does  not  require  careful  protection  from  the  saturated 
KC1  solution  usually  employed  as  a  liquid  junction  and  it  has  a 
high  conductivity  permitting  full  use  of  the  sensitivity  of  a  low- 
resistance  galvanometer.  It  differs  in  no  way  from  other  calomel 
half-cells  except  that  the  solution  is  saturated  with  KC1  in  the 
presence  of  solid  KC1  at  all  temperatures  used. 

There  is  not  very  good  agreement  between  the  values  assigned 
bo  the  saturated  calomel  half-cell  by  different  laboratories  and  it 
lad  therefore  best  be  regarded  for  the  time  being  as  a  good  work- 
ng-standard  to  be  checked  from  time  to  time  against  carefully 
nade  normal  or  tenth  normal  calomel  electrodes  or  against  a 
lydrogen  electrode  in  a  standard  solution.  For  ordinary  meas- 
urements however  the  values  given  in  table  a  of  the  Appendix 
„re  adequate. 


200 


THE  DETERMINATION  OF  HYDROGEN  IONS 


Michaelis  (1914)  gives  the  following  table  of  values  for  the  po- 
tential differences  referred  to  the  normal  hydrogen  electrode  for 
the  tenth  normal  and  the  saturated  calomel  electrodes. 


TABLE  43 


TEMPERATURE 

TENTH  NORMAL 

SATURATED 

% 

15 

0.2525 

16 

0.2517 

17 

0.2509 

18 

0.3377 

0.2503 

19 

0.2495 

20 

0.3375 

0.2488 

21 

0.2482 

22 

0  2475 

23 

0  2468 

24 

0  2463 

25 

0.2458 

30 

0.3364 

37 

0.2355 

38 

0.3355 

0.2350 

40 

0.3349 

50 

0.3326 

60 

0.3290 

SUPPLEMENTARY  REFERENCES 

Abegg  (1902),  Abegg-Auerbach-Luther  (1909),  Auerbach  (1912),  Bjerrum 
(1911),  Bugarszky  (1897),  Clarke-Myers-Acree  (1916),  Coggeshall 
(1895),  Coudres  (1892),  Ellis  (1916),  Fales-Vosburgh  (1918),  Lewis- 
Brighton-Sebastian  (1917),  Lewis-Sargent  (1909),  Lipscomb-Hulett 
(1916),  Loomis  (1915),  Loomis-Aeree  (1911),  Loomis-Meacham  (1916), 
Michaelis  (1914),  .Michaelis-David off  (1912),  Myers-Acree  (1913), 
Newberry  (1915),  Palmaer  (1907),  Richards  (1897),  Richards-Archi- 
bald (1902),  Sauer  (1904),  Steinwehr  (1905).  See  also  Chapter  XIX 
for  potential  values. 


CHAPTER  XIV 
The  Potentiometer  and  Accessory  Equipment 

The  method  usually  employed  in  the  measurement  of  potential 
differences  is  the  Poggendorf  compensation  method,  the  poten- 
tiometer method.  In  principle  it  consists  in  balancing  the  poten- 
tial difference  under  measurement  against  an  opposing,  known 
potential  difference.  When  the  unknown  is  so  balanced  no  cur- 
rent can  flow  from  it  through  a  current-indicating  instrument  such 
as  a  galvanometer. 

The  principle  may  be  illustrated  by  the  arrangement  shown  in 
figure  24  which  is  suitable  for  very  rough  measurements. 

According  to  modern  theory  the  conduction  of  electricity  in 
metals  is  the  flow  of  electrons,  the  electron  being  the  unit  electrical 
charge.  By  an  unfortunate  chance  the  two  kinds  of  electricity, 
which  were  recognized  when  a  glass  rod  was  rubbed  with  silk, 
were  given  signs  (+  for  the  glass  and  —  for  the  silk)  which  now 
leave  us  in  the  predicament  of  habitually  speaking  of  the  flow  of 
positive  electricity  when  the  evidence  is  for  the  flow  of  negative 
charges,  the  electrons.  But  so  far  as  the  illustration  of  principles 
is  concerned  it  makes  little  difference  and  we  shall  depart  from 
custom  and  shall  deal  with  the  negative  charges  in  order  to  make 
free  use  of  a  helpful  analogy.  We  may  imagine  the  electrons, 
already  free  in  the  metal  of  our  electrical  conductors,  to  be  com- 
parable with  the  molecules  of  a  gas  which  if  left  to  themselves 
will  distribute  themselves  uniformly  throughout  their  container 
(the  connected  metallic  parts  of  our  circuits).  We  may  now  im- 
agine the  battery  S  (fig.  24)  as  a  pump  maintaining  a  flow  of 
gas  (electrons)  through  pipes  (wires)  to  R  to  A  to  B  and  back  to 
S.  The  pipe  (wire)  AB  offers  a  uniform  resistance  to  the  flow 
so  that  there  is  a  uniform  fall  of  pressure  (potential)  from  A  to 
B  while  the  pump  (battery)  S  maintains  a  uniform  flow  of  gas 
(electrons).  If  we  lead  in  at  C  and  at  D  the  ends  of  the  pipes 
'wires)  from  another  pump  (battery)  X,  taking  care  that  the 
ligh  pressure  pipe  (wire)  from  X  leads  in  on  the  high  pressure 
dde  of  AB,  we  can  move  C,  D  or  both  C  and  D  until  they  span 

201 


202 


THE  DETERMINATION  OF  HYDROGEN  IONS 


a  length  of  AB  such  that  the  difference  of  pressure  (difference  of 
potential)  between  C  and  D  on  AB  is  equal  and  opposite  to  the 
difference  of  pressure  (difference  of  potential)  exerted  between 
C  and  D  by  X.  Then  no  current  can  flow  from  X  through  the 
current-indicating  instrument  G  and  we  thereby  know  that 
balance  is  attained. 

If  we  know  the  fall  of  electrical  potential  per  unit  length  along 
AB  the  difference  of  potential  exerted  by  X  will  be  known  from 
the  length  of  wire  between  C  and  D.  We  now  come  to  the  man- 
ner in  which  this  fall  of  potential  per  unit  length  is  determined. 


I    I    I    I    I    I    I    I    i    i    I    i    i    i 


Fig.  24.  Elementary  Potentiometer 

Choosing  for  units  of  electrical  difference  of  potential,  electrical 
resistance  and  electrical  current,  the  volt,  the  ohm,  and  the  am- 
pere respectively,  we  find  that  they  are  related  by  Ohm's  law: 

,.  N       Difference  in  potential  (in  volts) 

Current  (in  amperes)  = — — : ; : 

Resistance  (in  ohms) 


or 


R 


(41) 


With  this  relation  we  could  establish  the  fall  of  potential  along 
AB  by  measuring  the  resistance  of  AB  and  the  current  flowing. 
But  this  is  unnecessary,  for  we  have  in  the  Weston  cell  a  standard 


THE    POTENTIOMETER  203 

of  electromotive  force  (E.  M.  F.)  which  may  be  directly  applied 
in  the  following  manner.  The  unknown  X  (figure  24)  is  switched 
out  of  circuit  and  in  its  place  is  put  a  Weston  cell  of  known  E.  M.  F. 
Adjustment  of  C  and  D  is  made  until  the  "null  point"  is  attained, 
when  the  potential  difference  between  the  new  positions  of  C  and 
D  is  equal  to  the  E.  M.  F.  of  the  Weston  cell.  From  such  a  setting 
the  potential  fall  per  unit  length  of  AB  is  calculated.  It  must  be 
especially  noted  however  that  for  such  a  procedure  to  be  valid  the 
current  in  the  potentiometer  circuit  must  be  kept  constant  between 
the  operations  of  standardization  and  measurement  for  the  fundamen- 
tal relationship  upon  which  reliance  is  placed  is  that  of  Ohm's  law 

E 

C  =  — .     It  will  be  noted  that  the  establishment  of  the  difference 
R 

of  potential  between  any  two  points  on  AB  by  the  action  of  S 
and  the  resistance  of  AB  is  strictly  dependent  upon  the  relation 
given  by  Ohm's  law;  but,  since  we  draw  no  current  from  X  when 
balance  is  attained,  the  resistance  of  its  circuit  is  of  no  funda- 
mental importance.  It  only  affects  the  current  which  can  flow 
through  the  indicating  instrument  G  when  the  potential  differ- 
ences are  out  of  balance.  It  is  therefore  concerned  only  in  the 
sensitivity  of  G. 

The  simple  potentiometer  system  described  above  is  susceptible 
to  refinement  both  in  precision  and  in  convenience  of  operation. 

With  the  inevitable  variations  in  the  potentiometer  current 
which  occur  as  the  battery  runs  down  it  would  be  necessary  to 
recalculate  from  moment  to  moment  the  difference  of  potential 
per  unit  length  of  the  wire  AB  if  the  procedure  so  far  described 
were  used.  This  trouble  is  at  once  eliminated  if  the  contacts  of 
the  Weston  cell  can  be  thrown  in  at  fixed  points  and  the  current 
be  then  adjusted  by  means  of  the  rheostat  R  so  that  there  is  always 
the  same  uniform  current  producing,  through  the  resistance  be- 
tween the  Weston  cell  contacts,  the  potential  difference  of  this 
standard  cell.  Having  thus  arranged  for  the  adjustment  of  a 
uniform  current  at  all  times  and  having  the  resistance  of  AB 
already  fixed  it  is  now  permissible  to  calibrate  the  wire  AB  in 
terms  of  volts. 

In  the  Leeds  and  Northrup  potentiometer  (fig.  25),  the  resist- 
ance AB  of  our  elementary  instrument  (fig.  24)  is  divided  into  two 
sections  one  of  which  A-D  (fig.  25)  is  made  up  of  a  series  of 


204 


THE  DETERMINATION  OF  HYDROGEN  IONS 


resistance  coils  between  which  M  makes  contact  and  the  other 
portion  of  which  is  a  resistance  wire  along  which  M'  can  slide. 
When  the  potentiometer  current  has  been  given  the  proper  value, 
in  the  manner  which  will  be  described,  the  fall  of  potential  across 
any  one  of  the  coils  is  0.1  volt  so  that  as  M  is  shifted  from  the 
zero  point  D  the  potential  difference  between  M  and  D  is  increased 
0.1  volt  at  each  step.  Likewise,  when  the  current  is  in  adjust- 
ment, the  shifting  of  M'  away  from  D  increases  by  infinitesimal 
known  fractions  of  a  volt  the  difference  of  potential  between  M 
and  M'. 


+OscO- 


+  OEMfO- 


GA.  O 


Fig.  25.  Wiking  op  the  Leeds  and  Northrup  Potentiometer  (Type  K) 

Now  to  adjust  the  potentiometer  current  so  that  the  several  re- 
sistances in  the  potentiometer  circuit  will  produce  the  differences 
of  potential  in  terms  of  which  the  instrument  is  calibrated,  use  is 
made  of  the  Weston  cell  in  the  following  manner.  By  means  of 
a  switch,  U,  the  unknown  is  thrown  out  and  the  Weston  cell  is 
thrown  into  circuit.  One  pole  of  the  Weston  cell  circuit  is  fixed 
permanently.  The  other  can  be  moved  along  a  resistance  at  T 
constructed  so  that  the  dial  indicates  the  value  of  the  particular 
Weston  cell  in  use.  When  so  moved  to  agree  with  the  particular 
cell  in  use,  this  contact  at  T  is  left  in  its  position.  Now  the  current 
flowing  from  the  battery  W  is  adjusted  by  means  of  the  rheostat  R 


THE    POTENTIOMETER 


205 


until  the  difference  of  potential  between  T  and  0.5  balances  the 
potential  difference  of  the  Weston  cell  as  indicated  by  the  cessation 
of  current  in  the  galvanometer  GA.  The  resistance  T  to  "0.5"  is 
such  that  the  E.  M.  F.  of  the  battery  acting  across  this  resistance 
will  produce  the  desired  potentiometer  current.  This  current 
now  acting  across  the  several  resistances  furnishes  the  indicated 
potentials,  i.e.,  a  potential  difference  of  0.1  volt  across  each  coil. 
Another  arrangement  which  employs  the  ordinary  sets  of  re- 
sistances in  common  use  is  illustrated  in  figure  27. 


Fig.  26.  The  Leeds  and  Northrtjp  Potentiometer 

A  and  B  are  duplicate  sets  of  resistances  placed  in  series  with 
the  battery  S.  If  the  current  be  kept  uniform  throughout  this 
system  the  potential  difference  across  the  terminals  of  B  can  be 
varied  in  accordance  with  Ohm's  law  by  plugging  in  or  out  resist- 
ance in  B.  But  to  keep  the  current  constant  while  the  resistance  in 
B  is  changed  a  like  resistance  is  added  to  the  circuit  at  A  when  it 
is  removed  from  B,  and  removed  from  A  when  it  is  added  to  B. 

As  mentioned  before,  the  potential  difference  could  be  deter- 
mined from  the  resistance  in  B  and  a  measurement  of  the  current 
but  this  is  avoided  by  the  direct  application  of  a  Weston  cell  of 
known  potential.  Assuming  constant  current  a  Weston  cell 
replaces  X  and  adjustment  to  the  null  point  is  made  by  alter- 
ing the  resistance  in  B  with  compensation  in  A.  The  unknown 
is  then  thrown  into  circuit  and  adjustment  of  resistance  again 


206 


THE  DETERMINATION  OF  HYDROGEN  IONS 


made  to  the  null  point.  If  Ew  is  the  known  E.  M.  F.  of  the  Wes- 
ton cell,  Ex  the  potential  of  the  measured  cell,  Rw  the  resistance 
in  circuit  when  the  Weston  cell  is  in  balance  and  Rc  the  resistance 
in  circuit  when  the  measured  cell  is  in  balance  we  have 


Whence 


C  (constant)  =  —  =  — - 
Rc      Rv 


Ex  = 


EWRC 
Rw 


(42) 


Fig.  27.  Elementary  Resistance  Box  Potentiometer  System 

The  system  is  improved  by  providing  means  of  regulating  the 
potentiometer  current  till  constant  difference  of  potential  is  at- 
tained between  terminals  at  which  a  Weston  cell  may  be  thrown 
into  circuit.     Then  the  resistances  may  be  calibrated  in  volts. 

It  will  be  noted  that  in  this  arrangement  every  switch  or  plug 
contact  is  in  the  potentiometer  circuit.  A  bad  contact,  such  as  may 
be  produced  by  failure  to  seat  a  plug  firmly  during  the  plugging 
in  and  out  of  resistance,  or  by  corrosion  of  a  plug  or  dial  contact, 
will  therefore  seriously  affect  the  accuracy  of  this  potentiometer 
system.     It  requires  constant  care. 


THE    POTENTIOMETEB  207 

Lewis,  Brighton  and  Sebastian  (1917)  used  two  decade  resist- 
ance boxes  of  9999  ohms  each.  With  an  external  resistance  the 
current  was  adjusted  to  exactly  0.0001  ampere.  Thus  each  ohm 
indicated  by  the  resistance  boxes  when  balance  was  attained  cor- 
responded to  0.0001  volt.  Their  standard  cell  which  gave  at  25° 
1.0181  volts  was  spanned  across  B  (fig.  27)  and  182  ohms  of  the 
external  resistance. 

Another  mode  of  using  the  simple  system  illustrated  in  figure 
24  is  a  device  frequently  used  by  physicists,  and  introduced  into 
hydrogen  electrode  work  by  Sand  (1911)  and  again  by  Hilde- 
brand  (1913).  Instead  of  calibrating  unit  lengths  along  AD 
by  means  of  the  Weston  cell,  or  otherwise  applying  the  Weston 
cell  directly  in  the  system,  the  contacts  C  and  D  carry  the  terminals 
of  a  voltmeter.  When  balance  is  attained  this  voltmeter  shows 
directly  the  difference  of  potential  between  C  and  D,  and  there- 
fore the  E.  M.  F.  of  X.1 

A  diagram  of  such  an  arrangement  is  shown  in  figure  28.  There 
is  an  apparent  advantage  in  the  fact  that  the  Weston  cell  may  be 
dispensed  with  and  resistance  values  need  not  be  known.  There 
are  however  serious  limitations  to  the  precision  of  a  voltmeter  and 
in  two  cases  which  the  author  knows  accuracy  within  the  limited 
precision  of  the  instruments  was  attained  only  after  recalibration. 

A  voltmeter  is  generally  calibrated  for  potential  differences 
imposed  at  the  terminals  of  leads  supplied  with  the  instrument. 

Turning  again  to  figure  24  we  recall  that  when  any  given  fall 
of  potential  occurs  between  A  and  B,  a  definite  current  flows  in 
the  circuit  SRAB.  If  the  resistance  of  AB  is  known  a  measure 
of  the  current  flowing  permits  one  to  calculate  the  fall  of  potential 
between  A  and  B.  Thus  a  current-measuring  instrument  (am- 
meter) placed  in  series  with  the  fixed  resistance  AB  may  be  cali- 
brated to  indicate  differences  of  potential  between  A  and  B. 

1  It  is  sometimes  assumed  that  because  the  circuit  of  the  system  under 
measurement  is  placed  in  the  position  of  a  shunt  on  the  potentiometer  cir- 
cuit that  its  resistance  must  be  high  in  order  that  CD  (fig.  24)  may  indicate 
correctly  the  potential  difference.  The  fact  that  no  current  flows  in  this 
branch  when  balance  obtains  shows  clearly  that  its  resistance  can  have  no 
effect  on  the  accuracy  of  the  indication.  It  has  also  been  assumed  that  if 
CD  is  spanned  by  a  voltmeter,  the  resistance  of  the  voltmeter  should  be 
taken  into  consideration.  But  a  voltmeter  is  calibrated  to  always  indicate 
the  potential  difference  between  its  terminals. 


208 


THE   DETERMINATION    OF   HYDROGEN    IONS 


To  use  this  system  the  terminals  of  the  gas  chain  C  and  D  (fig. 
24)  are  moved  to  A  and  B  and  there  permanently  fixed.  An 
ammeter  is  placed  between  R  and  S  and  adjustment  of  R  is  made 
until  no  current  flows  in  G.  The  difference  of  potential  between 
A  and  B  as  indicated  by  the  calibrated  and  renamed  reading  of 
the  ammeter  is  then  equal  to  the  E.  M.  F.  of  the  gas  chain. 

Much  the  same  limitations  noted  in  the  voltmeter  system  apply 
to  the  ammeter  system. 


Fig.  28.  Voltmeter  Potentiometer  System 

A  modification  of  the  system  briefly  described  above  is  found 
in  the  "Pyrovolter."  The  essential  modification  is  a  device  of  wir- 
ing whereby  the  same  indicating  instrument  is  used  to  measure 
current  (indicated  in  volts)  and  to  indicate  the  null  point. 

In  a  few  instances  there  has  been  employed  a  system  of  measure- 
ment, the  principle  of  which  is  illustrated  in  the  wiring  diagram 
of  figure  29.  The  E.  M.  F.  of  a  gas  chain  is  allowed  to  charge 
a  fixed  condenser  c.  By  throwing  the  discharge  key  to  the  right 
the  charge  accumulated  by  the  condenser  is  allowed  to  discharge 
through  a  ballistic  galvanometer  b,  the  deflection  in  which  may  be 
made  a  measure  of  the  accumulated  charge  and  hence  of  the 
E.  M.  F.  of  the  gas  chain. 


THE   POTENTIOMETER 


209 


The  ballistic  galvanometer  is  one  designed  to  indicate  by  the 
angular  deflection  of  its  coil  the  quantity  of  electricity  passing 
through  the  coil  as  a  sudden  discharge.  The  quantity  of  elec- 
tricity stored  in  the  condenser  is  a  function  of  its  dimensions 
and  material  and  of  the  difference  of  potential  imposed  at  its 


hEMFh 


■'ig.  29.  Wiring  Diagram  Used  in  the  Ballistic  Galvanometer  System 


erminals.  The  dimensions  and  material  being  fixed  the  charge 
■ecomes  proportional  to  the  difference  of  potential.  Now  a 
(  efinite  difference  of  potential  may  be  imposed  by  means  of  the 
Veston  cell  w.  The  resulting  charge  in  the  condenser  is  discharged 
■  hrough  the  ballistic  galvanometer  giving  the  coil  a  definite 
(  eflection.  This  serves  to  calibrate  a  given  set-up  if  the  galva- 
)  ometer  is  so  designed  that  the  deflection  at  each  section  of  the 


210  THE   DETERMINATION    OF   HYDROGEN    IONS 

scale  is  proportional  to  the  quantity  of  electricity  discharged 
through  the  coil  and  if  the  wiring  be  such  that  no  serious  changes 
of  capacity  and  inductance  occur  in  manipulation. 

The  advantage  of. this  condenser  method  is  that  the  condenser 
may  be  conveniently  made  of  such  capacity  that  insignificant 
current  is  drawn  from  the  cell  under  measurement.  If  then  the 
technique  used  at  the  electrodes  is  refined  it  should  be  possible 
to  measure  equilibrium  potentials  which  would  be  easily  dis- 
placed by  current  withdrawal.  However,  until  there  are  pub- 
lished more  definite  data  relating  the  conditions  of  electrode 
measurements  to  the  theory  of  the  condenser  method,  this  system 
is  not  to  be  recommended  for  ordinary  use.  In  a  few  instances 
when  the  potentiometer  had  already  been  ad j  used  to  the  potential 
of  a  gas  chain  the  author  has  observed  what  appears  to  be  an 
excessive  E.  M.  F.  unsupported  by  the  equilibrium  conditions 
under  measurement.  This  disappears  after  an  initial  throw  of  the 
galvanometer  and  would  not  be  apparent  if  the  measurement  were 
being  made  by  adjusting  the  potentiometer  from  an  original 
position  sufficiently  out  of  balance  to  permit  a  very  sb'ght  current 
to  flow  during  successive  taps  of  the  key.  Will  such  E.  M.  F/s, 
which  are  evidently  temporary  and  do  not  represent  the  equilib- 
rium conditions  under  measurement,  be  recorded  in  the  ballistic 
galvanometer  method? 

Goode  (1922)  has  used  the  3-electrode  vacuum  valve  in  an 
arrangement  for  following  the  electromotive  forces  of  gas  chains. 

The  3-electrode  electron  tube  is  the  instrument  used  as  detec- 
tor and  amplifier  in  radio-communication  and  is  known  by  various 
names  such  as  "the  audion."  A  glass  bulb  (fig.  30)  exhausted 
to  a  very  low  gas  pressure  is  supplied  with  an  atmosphere  of  elec- 
trons by  their  emission  from  the  hot  filament  F.  These  electrons 
produce  what  may  be  called  a  space  charge  in  the  bulb.  Surround- 
ing the  filament  is  a  metallic  plate  P  which  can  be  maintained  at 
a  potential  about  22  volts  more  positive  than  the  filament  by 
means  of  the  battery  B.  Under  the  influence  of  this  fall  of  po- 
tential electrons  migrate  from  filament  to  plate,  producing  the 
so-called  plate-current.  But  interposed  in  this  electron-drift 
is  a  grid,  G,  of  wire  or  perforated  sheet  metal  through  which  the 
electrons  must  pass  in  their  migration  from  filament  to  plate. 
If  this  grid  is  charged  positively  with  relation  to  the  filament  it 


THE   POTENTIOMETER 


211 


will  tend  to  neutralize  the  space  charge  and  so  assist  the  filament- 
to-plate  current.  Conversely,  if  the  grid  is  charged  negatively 
with  relation  to  the  filament,  it  will  assist  the  space  charge 
and  so  tend  to  oppose  the  filament-to-plate  current. 

Thus  the  potential  difference  between  filament  and  grid,  a 
potential  difference  which  may  be  impressed  by  a  gas  chain  or 
other  cell,  can  govern  in  large  measure  the  filament-to-plate  stream 
of  electrons  and  a  measure  of  this  current  can  be  made  a  measure 
of  the  E.  M.  F.  of  the  cell,  C. 


•I' H*£ 


Fig.  30.  Wiring  of  Goode's  System  Employing  the  Electron  Tube 

Goode  considers  the  plate  current  Ip  to  be  made  up  of  a  con- 
stant current  IQ  characteristic  of  a  given  bulb  and  set  working 
conditions  and  a  current  Ip  —  IG  which  is  a  function  of  the  poten- 
tial difference  induced  by  C.  To  balance  I0  Goode  found  that 
with  the  particular  bulb  he  used  it  was  sufficient  to  place  a  vari- 
able resistance  R  between  the  positive  terminal  of  the  A  battery 
and  the  negative  terminal  of  the  B  battery  and  to  adjust  this 
resistance  till  the  galvanometer  Ga  was  at  its  zero  setting.  Under 
these  circumstances  the  deflection  of  Ga  becomes  a  function  of  the 


212  THE    DETERMINATION    OF   HYDROGEN    IONS 

grid  potential.  Within  the  range  of  E.  M.  F.  of  the  cells  under 
study  Goode  found  that  with  his  particular  apparatus  the  de- 
flection of  Ga  was  a  linear  function  of  IP  —  I0  when  Ga  was  shunted 
by  a  resistance  r  such  that  one  large  scale  division  corresponded 
to  one  unit  of  pH. 

Goode  claims  that  the  unique  advantage  of  his  system  consists 
in  the  fact  that  so  little  current  is  drawn  from  the  cell  C  that 
continuous  readings  may  be  made.  This  system  should,  there- 
fore, prove  useful  in  studying  those  drifts  of  electrode  potential 
which  occur  in  a  variety  of  cases  and  which  need  more  thorough 
investigation. 

For  the  more  refined  uses  to  which  Goode's  system  may  be 
put  it  will  be  necessary  either  to  know  the  characteristics  of  the 
bulb  in  use  or  else  to  carefully  calibrate  a  given  apparatus. 

The  electron  tube,  when  used  as  a  valve  for  amplification, 
should  be  useful  in  making  hydrogen  electrode  differences  of 
potential  control  mechanical  devices  such  as  alkali  or  acid  feeds 
for  continuous  commercial  processes. 

NULL   POINT   INSTRUMENTS 

Referring  to  figure  24  and  the  accompanying  text  the  reader  will 
see  that  in  the  balancing  of  potential  differences  by  the  Poggen- 
dorf  compensation  method  there  is  required  a  current  indicating 
instrument  to  determine  the  null  point.  Such  instruments  will 
be  briefly  described,  and  some  of  their  characteristics  discussed. 

The  galvanometer  is  a  current-indicating  instrument,  which,  in 
the  form  most  useful  for  the  purpose  at  hand,  consists  of  a  coil  of 
wire  in  the  magnetic  field  of  a  strong  permanent  magnet.  This 
coil  is  connected  into  the  circuit  in  which  the  presence  or  absence 
of  current  is  to  be  detected.  A  current  flowing  through  the  turns 
of  the  suspended  coil  produces  a  magnetic  field  in  its  interaction 
with  the  field  of  the  permanent  magnet  and  tends  to  turn  the  coil 
so  that  it  will  embrace  the  maximum  number  of  lines  of  force. 
The  construction  of  galvanometers  need  not  be  discussed  since  it 
is  a  matter  for  instrument  makers,  but  certain  desirable  qualities 
will  be  treated  in  a  later  section,  together  with  the  characteristics 
of  other  instruments. 

Provision  should  be  made  for  the  mounting  of  a  galvanometer 


THE    POTENTIOMETER 


213 


where  it  will  receive  the  least  vibration.  If  the  building  is  sub- 
jected to  troublesome  vibrations  some  sort  of  rubber  support 
may  be  interposed  between  the  galvanometer  mounting  and  the 
wall  bracket  or  suspension.  Three  tennis  balls  held  in  place  by 
depressions  in  a  block  of  wood  on  which  the  galvanometer  is 
placed  may  help.  In  some  instances  the  more  elaborate  Julius 
suspension  such  as  those  advertised  may  be  necessary. 


Fia.  31.  A  Galvanometer 

The  capillary  electrometer  depends  for  its  action  upon  the  altera- 
ion  of  surface  tension  between  mercury  and  sulfuric  acid  with 
.Iteration  of  the  potential  difference  at  the  interface.  A  simple 
orm  suitable  for  that  degree  of  precision  which  does  not  call  for 
he  advantages  of  a  galvanometer  is  illustrated  in  figure  32. 

Platinum  contacts  are  sealed  into  two  test  tubes  and  the  tubes 
j  re  joined  as  illustrated  by  means  of  a  capillary  K  of  about  1  mm. 
( iameter.  In  making  the  seals  between  capillary  and  tubes  the 
(  apillary  is  first  blown  out  at  each  end  and  can  then  be  treated  as 
i  tube  of  ordinary  dimensions  in  making  a  T  joint.     After  a  thor- 


214  THE    DETERMINATION    OF   HYDROGEN   IONS 

ough  cleaning  the  instrument  is  filled  as  illustrated  with  clean,  dis- 
tilled mercury,  sufficient  mercury  being  poured  into  the  left  tube 
to  bring  the  meniscus  in  the  capillary  near  a  convenient  point. 
In  the  other  tube  is  now  placed  a  solution  of  sulfuric  acid  made 
by  adding  5.8  cc.  water  to  10  cc.  sulfuric  acid  of  1.84  specific 
gravity.  The  air  is  forced  out  of  the  capillary  with  mercury 
until  a  sharp  contact  between  mercury  and  acid  occurs  in  the 
capillary.  The  instrument  is  now  mounted  before  a  microscope 
using  as  high  power  lenses  as  the  radius  of  the  glass  capillary  will 
permit.  The  definition  of  the  mercury  meniscus  is  brought  out 
by  cementing  to  the  capillary  with  Canada  balsam  a  cover  glass 
as  illustrated. 

An  important  feature  in  the  use  of  the  capillary  electrometer 
is  its  short  circuiting  between  measurements.  This  is  done  by  the 
key  shown  in  figure  32.  Tapping  down  on  the  key  breaks  the  short- 
circuit  and  brings  the  terminals  of  the  electrometer  into  circuit 
with  the  E.  M.  F.  to  be  balanced.  If  the  E.  M.  F.  is  out  of  bal- 
ance the  potential  difference  at  the  mercury-acid  interface  causes 
the  mercury  to  rise  or  fall  in  the  capillary.  Releasing  the  key 
short-circuits  the  terminals  and  allows  the  mercury  to  return  to 
its  normal  position.  Adjustment  of  the  potentiometer  is  con- 
tinued till  no  movement  of  the  mercury  can  be  detected.  To 
establish  a  point  of  reference  from  which  to  judge  the  movement 
of  the  mercury  meniscus  the  microscope  should  contain  the  fa- 
miliar micrometer  disk  at  the  diaphragm  of  the  eye  piece.  In 
lieu  of  this  an  extremely  fine  drawn  thread  of  glass  or  a  spider  web 
may  be  held  at  the  diaphragm  of  the  eye  piece  by  touches  of  Can- 
ada balsam. 

The  quadrant  electrometer  is  so  little  used  as  a  null  point  instru- 
ment that  only  a  brief  description  will  be  given.  In  the  form 
useful  for  the  purpose  at  hand  a  very  light  vane  of  aluminium  is 
suspended  by  an  extremely  fine  thread,  preferably  of  quartz, 
which  is  metalized  on  the  surface  in  order  to  conduct  charges  to 
the  vane.  The  vane  is  surrounded  by  a  flat,  cylindrical  metal 
box  cut  into  quadrants.  Two  opposite  quadrants  are  connected 
to  one  terminal  and  the  remaining  quadrants  to  another  terminal. 
If  now  the  vane  or  needle  be  charged  from  one  terminal  of  a 
high-voltage  battery  the  other  terminal  of  which  is  grounded, 
and  a  difference  of  potential  be  established  between  the  two  sets 


THE    POTENTIOMETER 


215 


of  quadrants,  the  needle  will  be  deflected  by  the  electrostatic 
forces  imposed  and  induced.  When  used  as  a  null  point  instru- 
ment in  connection  with  the  potentiometer  the  two  sets  of  quad- 
rants may  be  connected  as  are  the  terminals  of  the  capillary 
electrometer  and  spanned  by  a  short-circuiting  key. 


Fig.  32.  Diagram  of  Capillary  Electrometer  and  Key 


Since  the  current  drawn  for  its  operation  is  only  the  amount 
lecessary  to  charge  a  system  of  very  low  capacity  to  the  low  po- 
ential  difference  when  the  potentiometer  is  slightly  out  of  bal- 
ance with  the  measured  E.  M.  F.  (and  to  zero  potential  difference 


216  THE   DETERMINATION   OF    HYDROGEN    IONS 

at  balance)  the  quadrant  electrometer  might  be  of  special  value 
in  the  study  of  easily  displaced,  electrode  equilibria.  However, 
the  attainment  of  the  desired  sensitivity  with  some  of  these  in- 
struments is  a  task  requiring  great  skill  and  patience.  Further- 
more the  rated  sensitivity  is  sometimes  attained  by  adjusting  the 
so-called  electrostatic  control  to  such  a  value  that  the  zero  posi- 
tion of  the  needle  is  rendered  highly  unstable.  This  combined 
with  the  very  long  period  at  high  sensitivity  renders  the  instru- 
ment unsatisfactory  for  common  use.  Against  these  objections 
are:  first,  the  point  mentioned  above,  and  second  the  advantage 
that  the  instrument  may  ordinarily  be  left  in  circuit  during  the 
adjustment  of  the  potentiometer  as  is  not  the  case  with  the 
galvanometer. 

Telephone  receiver.  The  modern  high  resistance  telephone  re- 
ceiver of  the  type  used  in  radio  reception  may  serve  in  an  emer- 
gency [Kiplinger  (1921)].  Lack  of  balance  between  potentiometer 
adjustment  and  measured  E.  M.  F.  is  indicated  by  a  click  in  the 
receiver  when  the  potentiometer  key  is  tapped;  but  there  is  of 
course  nothing  but  the  loudness  of  the  click  to  show  how  far  from 
balance  the  adjustment  is,  and  only  the  decrement  of  the  sound 
to  indicate  that  adjustment  in  the  proper  direction  is  being  made. 

Selection  of  null  point  indicators.  In  the  selection  of  instru- 
ments for  the  measurement  of  the  electromotive  force  of  gas 
chains  it  is  desirable  that  there  should  be  a  balancing  of  instru- 
mental characteristics  and  the  selection  of  those  best  adapted  to 
the  order  of  accuracy  required.  A  null  point  instrument  of  low 
sensitivity  may  annul  the  value  of  a  well-designed,  expensive  and 
accurate  potentiometer;  and  a  galvanometer  of  excessive  sensi- 
tivity may  be  very  disconcerting  to  use.  The  potentiometer  sys- 
tem and  the  null  point  instrument  should  be  adapted  one  to  the 
other  and  to  their  relation  to  the  system  to  be  measured. 

The  several  corrections  which  have  to  be  found  and  applied  to 
accurate  measurements  of  hydrogen  electrode  potentials  are 
matters  of  a  millivolt  or  two  and  fractions  thereof.  Collectively 
they  may  amount  to  a  value  of  the  order  of  5  millivolts.  Whether 
or  not  such  corrections  are  to  be  taken  into  account  is  a  question 
the  answer  to  which  may  be  considered  to  determine  whether  a 
rough  measuring  system  or  an  accurate  one  is  to  be  used.  For  all 
"rough"  measurements  the  capillary  electrometer  is  a  good  null 


THE    POTENTIOMETER  217 

point  instrument.  It  has  a  very  high  resistance  which  hinders 
the  displacement  of  electrode  equilibria  at  unbalance  of  a  crude 
potentiometer  system.  It  is  easily  constructed  by  anyone  with 
a  knowledge  of  the  elements  of  glass  blowing,  and  without  par- 
ticular care  may  be  made  sensitive  to  0.001  volt. 

For  "accurate"  measurements  there  is  little  use  in  making  an 
elaborate  capillary  electrometer  or  in  temporizing  with  poor 
galvanometers. 

The  apportionment  of  galvanometer  characteristics  is  a  compli- 
cated affair  which  must  be  left  in  the  hands  of  instrument  makers, 
but  there  are  certain  relations  which  should  be  fulfilled  by  an  in- 
strument to  be  used  for  the  purpose  at  hand,  and  general  knowledge 
of  these  is  quite  necessary  in  selecting  instruments  from  the  wide 
and  often  confusing  variety  on  the  market. 

Galvanometer  sensitivities  are  expressed  in  various  ways. 
Since  one's  attention  is  centered  upon  detecting  potential  differences 
the  temptation  is  to  ask  for  the  galvanometer  sensitivity  in  terms 
)f  microvolt  sensitivity.  There  are  two  ways  of  expressing  this 
vhich  lead  to  different  values.  One  is  the  deflection  caused  by  a 
nicrovolt  acting  at  the  terminals  of  the  galvanometer.  The 
nore  useful  value  is  the  deflection  caused  by  a  microvolt  acting 
hrough  the  external  critical  damping  resistance.  But  in  the  last 
analysis  the  instrument  is  to  be  used  for  the  detection  of  very 
!  mall  currents  and  these  currents  when  allowed  to  flow  through  the 
j  ;alvanometer  by  the  unbalancing  of  the  circuit  at  a  slight  poten- 
lial  difference  are  determined  by  the  total  resistance  of  the  gal- 
vanometer circuit.  The  instrument  might  be  such  that  a  micro- 
volt at  the  terminals  would  cause  a  wide  deflection,  while,  if 
1  Dreed  to  act  through  a  large  external  resistance,  this  microvolt 
^  'ould  leave  the  galvanometer  "dead. "  For  this  reason  it  is  best 
t  d  know  the  sensitivity  in  terms  of  the  resistance  through  which  a 
i  nit  voltage  will  cause  a  given  deflection.  This  is  the  megohm 
sensitivity  and  is  defined  as  "the  number  of  megohms  (million 
c  hms)  of  resistance  which  must  be  placed  in  the  galvanometer 
c  rcuit  in  order  that  from  an  impressed  E.  M.  F.  of  one  volt  there 
s  lall  result  a  deflection  of  one  millimeter"  upon  a  scale  one 
r  ieter  from  the  reflecting  mirror  (Leeds  and  Northrup  catalogue 
2 ),  1918).  The  numerical  value  of  this  megohm  sensitivity  also 
r  ^presents  the  microampere  sensitivity  if  this  is  defined  as  the 
e  imber  of  millimeters  deflection  caused  by  one  microampere. 


218         THE  DETERMINATION  OF  HYDROGEN  IONS 

In  hydrogen  electrode  measurements  the  resistance  of  the  cells 
varies  greatly  with  design  (length  and  width  of  liquid  conductors) 
and  with  the  composition  of  the  solutions  used  (e.g.  saturated  or 
M/10  KC1).  Constricted,  long  tubes  may  raise  the  resistance  of 
a  chain  so  high  as  to  annul  the  sensitivity  of  a  galvanometer  unless 
this  has  a  high  megohm  sensitivity.  Dr.  Klopsteg  (private  com- 
munication) states  that  the  resistance  of  the  galvanometer  coil 
ideally  should  be  of  about  the  same  order  of  magnitude  as  that 
of  the  cell  to  be  measured  if  maximum  sensitivity  is  to  be  gained. 
Here  however  we  enter  complexities,  since  the  arrangements  by 
which  high  megohm  sensitivity  is  attained  affect  other  galva- 
nometer characteristics.  One  of  these,  which  is  not  essential  but 
is  desirable,  is  a  short  period.  A  short  period  facilitates  the  set- 
ting of  a  potentiometer.  If  the  circuits  are  out  of  balance,  as  they 
generally  are  at  the  beginning  of  a  measurement,  the  direction  for 
readjustment  may  be  inferred  from  the  direction  of  galvanometer 
deflection  without  bringing  the  coil  back  each  time  to  zero  setting, 
but  there  comes  a  time  when  prompt  return  to  zero  setting  is 
essential  to  make  sure  that  slight  resettings  of  the  potentiometer 
are  being  made  in  the  proper  direction. 

For  a  return  of  the  coil  to  zero  without  oscillation  it  is  neces- 
sary to  have  some  sort  of  damping.  This  is  generally  a  shunt 
across  the  galvanometer  terminals,  the  so-called  critical  damping 
resistance.  This  shunt  permits  a  flow  of  current,  when  the  main 
galvanometer  circuit  is  opened,  which  is  generated  by  the  turning 
of  the  coil  in  the  magnetic  field.  The  magnetic  field  produced  in 
the  coil  by  this  current  interacting  with  the  field  of  the  perman- 
ent magnet  tends  to  oppose  the  further  swing  of  the  coil.  When 
the  resistance  of  the  shunt  is  so  adjusted  to  the  galvanometer 
characteristics  that  the  swing  progresses  without  undue  delay  to 
zero  setting  and  there  stops  without  oscillation,  the  galvanometer 
is  said  to  be  critically  damped.  Critical  damping  as  applied  to 
deflection  on  a  closed  circuit  need  not  be  considered  when  the 
galvanometer  is  used  as  a  null  point  instrument.  Since  some  of 
the  best  galvanometers  are  not  supplied  with  a  damping  resist- 
ance the  purchaser  of  an  outfit  for  hydrogen  electrode  work  should 
take  care  to  see  that  he  includes  the  proper  unit.  Underdamped 
and  overdamped  instruments  will  prove  very  troublesome  or 
useless. 


THE    POTENTIOMETER  219 

These  very  brief  considerations  are  presented  merely  as  an  aid 
in  the  selection  of  instruments.  The  manner  in  which  desirable 
qualities  are  combined  is  a  matter  of  considerable  complexity  but 
fortunately  makers  are  coming  to  appreciate  the  very  simple  but 
important  requirements  for  hydrogen  electrode  work  and  are 
prepared  to  furnish  them.  The  galvanometer  now  in  use  by  the 
author  has  the  following  characteristics;  coil  resistance  530  ohms, 
critical  damping  resistance  9,000  ohms,  period  6  seconds,  sen- 
sitivity 2245  megohms.  It  is  not  the  ideal  instrument  for  the 
hydrogen  electrode  system  in  use  but  is  satisfactory.  A  shorter 
period  is  desirable  and  a  higher  coil  resistance  to  correspond 
better  with  the  average  resistance  of  the  order  of  one  to  two 
thousand  ohms  in  some  gas  chains,  would  be  desirable;  but  im- 
provement in  both  of  these  directions  at  the  same  time  may  in- 
crease the  expense  of  the  instrument  beyond  the  practical  worth. 
Indeed  certain  instruments  now  on  the  market  are  satisfactory 
for  almost  any  type  of  hydrogen  electrode  measurements. 

In  using  a  galvanometer  it  is  important  to  remember  that  while 
the  E.  M.  F.  of  a  cell  is  unbalanced  its  circuit  should  be  left  closed 
only  long  enough  to  show  the  direction  of  the  galvanometer  deflec- 
tion. Otherwise  current  will  flow  in  one  direction  or  the  other 
through  the  chain  and  tend  to  upset  the  electrode  equilibrium. 
A  mere  tap  on  the  key  which  closes  the  galvanometer  circuit  is 
sufficient  till  balance  is  obtained. 

Of  potentiometer  characteristics  little  need  be  said  for  the  choice 
in  the  first  instance  will  lie  between  instruments  sold  by  reliable 
makers.  In  the  second  instance  the  choice  will  lie  between 
instruments  of  different  range  and  many  of  the  unique  instruments 
may  be  at  once  eliminated  by  a  calculation  which  shows  that  the 
reputed  accuracy  involves  too  close  a  scale  reading  to  be  reliable. 
Certain  difficulties  which  enter  into  the  construction  of  potentio- 
meters for  accurate  thermo-couple  work  are  hardly  significant 
for  the  order  of  accuracy  required  of  hydrogen  electrode  work. 
The  range  from  zero  to  1.2  volts  and  the  subdivisions  0.0001 
volt  do  for  measurements  of  ordinary  accuracy.  There  should 
be  a  variable  resistance  to  accomodate  the  variations  in  individual 
Weston  cells  of  from  1.0175  to  1.0194  volts,  and  provision  for 
quickly  and  easily  interchanging  Weston  cell  with  measured 
E.  M.  F. 


220         THE  DETERMINATION  OF  HYDROGEN  IONS 

Several  of  the  features  of  standard  potentiometers  may  be  elim- 
inated without  injury  to  their  use  for  hydrogen  electrode  measure- 
ments and  would  reduce  their  cost.  Steps  in  this  direction  have 
been  taken  by  at  least  one  manufacturer. 

Having  described  the  fundamental  principles  of  the  potentio- 
meter it  seems  hardly  worth  while  to  discuss  the  numerous  modi- 
fications found  among  manufactured  instruments  or  used  in  the 
construction  of  home-made  designs.  With  the  advent  into  every 
town  of  the  numerous  and  varied  parts  of  radio  apparatus  cer- 
tain accessory  parts  of  a  potentiometer  may  be  readily  purchased 
and  the  amateur  can  concentrate  his  attention  upon  the  essential 
resistances.  But,  unless  he  is  equipped  to  make  these  with  accur- 
acy and  to  mount  them  with  care,  he  may  waste  the  cost  of  a 
satisfactory  instrument. 

With  regard  to  the  more  special  or  unique  designs  found  on 
the  market  it  may  simply  be  said  that  they  were  developed  for 
special  purposes  and  that  unless  these  special  purposes  are  to  be 
accomodated,  the  purchaser  will  do  well  to  depend  only  upon  an 
instrument  of  universal  applicability. 

When  rubber  is  used  as  the  insulating  material  of  instruments 
employed  as  potentiometers  the  rubber  should  not  be  left  exposed 
to  the  light  unduly.  The  action  of  the  light  not  only  injures 
the  appearance  of  the  rubber  but  also  may  cause  the  formation 
of  conducting  surface  layers. 

If  the  potentiometer  system  contains  a  sliding  contact  and 
this  contact  is  not  involved  in  the  resistance  of  the  primary  poten- 
tiometer circuit  proper,  the  contact  should  be  kept  heavily  coated 
with  pure  vaseline.  If  there  be  any  doubt  whatever  about  the 
quality  of  this  vaseline  it  should  be  boiled  with  several  changes 
of  distilled  water,  skimmed  off  when  cool  and  then  thoroughly 
dried.  If  this  is  done  there  will  seldom  be  any  need  to  resort  to 
the  heroic  and  dangerous  procedure  of  polishing. 

It  cannot  be  too  strongly  emphasized  that  while  a  low  order 
of  precision  is  often  adequate  for  a  certain  purpose  the  employ- 
ment of  crude  measuring  instruments  often  obscures  the  data  of 
greatest  significance.  This  statement  should  not  be  interpreted 
as  a  discouragement  to  those  who  are  about  to  undertake  measure- 
ments with  some  such  system  as  that  illustrated  in  figure  28  for 
important  data  have  been  obtained  with  just  such  instruments. 


THE    POTENTIOMETER  221 

The  statement  is  intended  rather  as  an  encouragement  to  the 
beginner  who  will  find  the  handling  of  more  precise  instruments 
easy  and  the  rewards  rich. 

THE    WESTON     CELL 

The  elementary  construction  of  the  Weston  cell  is  shown  in 
figure  33.  The  mercury  in  the  left  arm  should  be  carefully  puri- 
fied (page  239)  and  the  same  material  should  be  used  for  the 
preparation  of  the  cadmium  amalgam.  This  amalgam  consists 
of  12.5  per  cent  by  weight  of  electrolytic  cadmium.  The  amal- 
gam is  formed  by  heating  mercury  over  a  steam  bath  and  stirring 
in  the  cadmium.  Any  oxid  formed  may  be  strained  off  by  pouring 
the  molten  amalgam  through  a  test  tube  drawn  out  to  a  long 
capillary. 

Cadmium  sulfate  may  be  recrystallized  as  described  by  Wolff  and 
Waters  (1907).  Dissolve  in  excess  of  water  at  70°C,  filter,  add 
excess  of  basic  cadmium  sulfate  and  a  few  cubic  centimeters  of  hy- 
drogen peroxid  to  oxidize  ferrous  iron,  and  heat  several  hours. 
Then  filter,  acidify  slightly  and  evaporate  to  a  small  volume.  Fil- 
ter hot  and  wash  the  crystals  with  cold  water.  Recrystallize 
slowly  from  an  initially  unsaturated  solution.  The  cadmium  sul- 
fate solution  of  a  "normal"  Weston  cell  is  a  solution  saturated  at 
whatever  temperature  the  cell  is  used,  and  therefore  the  cell  should 
contain  crystals  of  the  sulfate.  The  ordinary  unsaturated  cell 
has  a  cadmium  sulfate  solution  that  is  saturated  at  about  4°C. 

In  the  study  of  Weston  cells  considerable  attention  has  been 
paid  to  the  quality  of  the  mercurous  sulfate.  Perhaps  the  best 
and  at  the  same  time  the  most  conveniently  prepared  material  is 
that  made  electrolytically.  Where  the  alternating  current  is 
available  it  is  preferable  to  use  it.  A  good  average  set  of  condi- 
tions is  a  sixty  cycle  alternating  current  sent  through  a  25  per  cent 
sulfuric  acid  solution  with  a  current  density  at  the  electrodes  of 
5  to  10  amperes  per  square  decimeter.  With  either  the  alternat- 
ing or  direct  current  the  apparatus  described  on  page  192  is 
3onvenient. 

In  the  Weston  cell  the  lead-in  wires  of  platinum  should  be 
imalgamated  electrolytically  by  making  a  wire  the  cathode  in  a 
solution  of  pure  mercurous  nitrate  in  dilute  nitric  acid. 


222 


THE  DETERMINATION  OF  HYDROGEN  IONS 


After  filling  the  cell  it  may  be  sealed  off  in  the  blast  flame  or 
corked  and  sealed  with  wax. 

Since  the  preparation  of  a  good  Weston  cell  is  a  matter  of  con- 
siderable detail,  since  such  cells  must  be  properly  and  carefully 
made  in  order  to  establish  the  true  potential  differences  in  a  poten- 
tiometer system,  and  since  reliable  cells  of  certified  values  may  be 
purchased  at  a  reasonable  price,  it  hardly  pays  the  individual 
investigator  to  construct  his  own.  It  would,  however,  be  a  con- 
venience if  the  materials  could  be  purchased  of  the  Bureau  of 
Standards  as  was  once  proposed. 

In  some  portable  Weston  cells  of  commerce  the  mercury  is 
introduced  as  amalgamated  electrodes  and  the  cadmium  sulfate 
solution,  instead  of  being  always  in  the  presence  of  cadmium 
sulfate  crystals,  is  often  saturated  at  about  4°C.  Since  this  leaves 
the  solution  unsaturated  at  ordinary  temperatures  this  cell  is 


Hgzso7 

Hg 


mm 


CdSO. 


Hg-Cd 


•      Fig.  33.  Diagram  of  the  Weston  Standard  Cell 

sometimes  called  the  "unsaturated"  type.  The  result  is  a  cell 
having  a  much  lower  temperature  coefficient  than  that  of  the 
"normal"  cell.  There  remain,  however,  large,  if  opposite,  tem- 
perature coefficients  for  the  two  arms;  and  it  is  therefore  necessary 
to  protect  the  cell  from  temperature  changes  which  will  affect 
the  two  arms  unequally.  Furthermore  in  all  Weston  cells  there 
may  be  observed  some  degree  of  hysteresis  and  in  particular 
cases  this  may  be  very  marked.  It  is  therefore  advisable  under 
all  circumstances  to  protect  any  Weston  cell  from  temperature 
fluctuations. 

Weston  cells  are  standardized  in  terms  of  the  international  volt 
the  secondary  standard  for  which  is  the  average  E.  M.  F.  of 


THE    POTENTIOMETER 


223 


"normal"  Weston  cells  maintained  at  each  national  standards 
laboratory. 

As  the  result  of  cooperative  measurements  by  the  national 
standards  laboratories  of  England,  France,  Germany  and  the 
United  States  the  value  1.01830  international  volts  at  20°C.  was 
assigned  to  the  "normal"  Weston  cell.  The  United  States  Bu- 
reau of  Standards  maintains  a  group  of  these  normal  Weston  cells 
whose  mean  value  is  taken  as  1.0183  international  volts  and  serves 
for  the  standardization  of  the  commercial  cells.  It  is  important 
to  note  that  this  international  agreement  came  into  force  January 
1,  1911,  and  that  prior  to  that  time  the  values  in  force  in  different 
countries  varied  considerably. 

TABLE  44 


TEMPERATURE 

DIFFERENCE 

°c. 

0 

+0.000,359 

5 

+0.000,366 

10 

+0.000,304 

15 

+0.000,179 

20 

0.000,000 

25 

-0.000,226 

30 

-0.000,492 

35 

-0.000,791 

40 

-0.001,114 

The  temperature  coefficient  of  the  "normal"  Weston  cell  is 
;iven  by  Wolff  (1908)  as: 

Et  =  Esq  -  0.000,040,75  (t  -  20)  -  0.000,000,944  (t  -  20)2  + 
0.000,000,009,8  (t  -  20)3  (43) 

3y  this  formula  the  differences  in  volts  from  the  20°  value  are  as 
;iven  in  table  44. 

In  other  words  a  normal  Weston  cell  should  have  its  certified 
/alue  corrected  by  addition  of  the  above  corrections  when  used  at 
emperatures  other  than  20°C.  But  an  "unsaturated"  Weston  cell 
nay  for  all  ordinary  purposes  be  considered  as  having  no  tempera- 
ure  coefficient  and  its  certified  value  may  therefore  be  used  as 
;  ;iven  for  all  moderate  variations  from  20°C.  The  change  in  E.  M. 
<\  of  the  unsaturated  type  is  less  than  0.000,01  volt  per  degree, 


224  THE    DETERMINATION    OF   HYDROGEN   IONS 

provided    the    precautions    regarding    temperature    fluctuations 
previously  mentioned  are  observed. 

While  most  commercial  cells  are  of  the  "unsaturated"  type, 
the  purchaser  should  be  informed  whether  a  given  cell  is  of  the  one 
type  or  the  other. 

STORAGE   BATTERIES 

The  storage  battery  or- accumulator  is  a  convenient  and  reli- 
able source  of  current  for  the  potentiometer.  Standard  poten- 
tiometers are  generally  designed  for  use  with  a  single  cell  which 
gives  an  E.  M.  F.  of  about  two  volts. 

The  more  familiar  cell  to  which  our  attention  shall  be  confined 
consists  of  two  series  of  lead  plates  immersed  in  a  sulfuric  acid 
solution  of  definite  specific  gravity.  The  plates  of  one  series  are 
connected  to  one  pole  of  the  cell  and  the  plates  of  the  other  series 
are  connected  to  the  other  pole.  When  a  current  is  passed  through 
the  cell  it  will  produce  lead  peroxid  upon  the  plates  by  which  the 
positive  current  enters  and  spongy  lead  upon  the  other  plates.  On 
charging,  therefore,  the  plates  in  connection  with  the  positive  pole 
assume  the  brown  color  of  the  oxid  while  the  plates  in  connection 
with  the  negative  pole  assume  the  slate  color  of  the  spongy  metal. 
The  poles  should  be  distinctly  marked  so  that  one  need  not  inspect 
the  plates  to  distinguish  the  polarity  but  should  the  marks  become 
obscured  and  the  cell  be  a  closed  cell  the  polarity  should  be  care- 
fully tested  with  a  voltmeter  before  attaching  the  charging  cur- 
rent. In  lieu  of  a  voltmeter  the  polarity  may  be  tested  with  a 
paper  moistened  with  KI  solution.  On  applying  the  terminals 
to  the  paper  a  brown  stain  is  produced  at  the  positive  pole, — 
positive  reaction  at  positive  pole. 

In  charging  a  cell  the  positive  pole  of  the  charging  circuit  should 
be  connected  to  the  positive  terminal  of  the  cell,  else  the  cell  will 
be  ruined.  If  a  direct  current  lighting  circuit  is  available,  it  may 
be  used  to  charge  a  cell,  or  battery  of  cells,  provided  sufficient 
resistance  be  placed  in  series.  A  16-candle-power  carbon  filament 
on  a  110-volt  circuit  allows  about  half  an  ampere  to  pass.  A 
bank  of  6  lamps  in  parallel  will  allow  three  amperes  to  pass  if 
we  neglect  the  battery  resistance.  Ordinarily  one  will  do  well 
to  charge  at  a  rate  lower  than  that  specified  by  the  maker,  for  the 


THE    POTENTIOMETER  225 

care  of  a  battery  consists  chiefly  in  keeping  the  deposits  even. 
Low  rates  of  charge  and  discharge  favor  this.  On  charging,  the 
voltage  will  rise  rapidly  to  2.35  volts  where  it  will  remain  during 
the  greater  part  of  the  period.  When  it  rises  to  2.5  volts  the 
charging  should  be  discontinued.  It  is  when  it  has  reached  this 
voltage  that  the  cell  will  "gas"  vigorously.  If  a  cell  should  fail 
to  "gas"  after  a  reasonable  time  it  may  have  an  internal  short 
circuit  due  to  warping  of  the  plates  or  the  scaling  of  conducting 
material.  In  searching  for  such  a  condition  a  wooden  pry,  never 
a  metallic  one,  should  be  used.  Careful  handling  and  charging 
will  generally  prevent  such  short  circuits. 

It  is  more  economical  to  charge  from  a  low  voltage  circuit  but 
this  is  seldom  available.  Indeed  there  is  often  available  only  an 
alternating  current  of  lighting-circuit  voltage.  To  use  the  energy 
of  an  alternating  current  it  must  either  be  used  with  a  motor 
generator  furnishing  a  direct  current  (preferably  of  low  voltage) 
or  else  rectified.  There  are  now  readily  available  a  variety  of 
rectifiers  used  in  charging  the  batteries  of  radio  amateurs.  Most 
of  these  rectifiers  when  of  the  mechanical  type  are  designed  for 
charging  a  six-volt  battery.  If  the  operator  of  a  hydrogen  elec- 
trode has  a  two-volt  cell  for  his  potentiometer  and  a  four-volt 
battery  for  operating  the  relay  of  the  temperature  control  sys- 
tem he  has  a  combination  suited  to  the  common  and  inexpensive 
type  of  rectifier. 

In  the  discharging  of  a  cell  the  sulfuric  acid  is  converted  to  sul- 
fate which  is  deposited.     The  result  is  the  lowering  of  the  specific 
gravity  of  the  battery  liquid.     Thus  the  specific  gravity  of  the 
liquid  is  highest  when  the  battery  is  fully  charged  and  lowers  on 
discharging.     If  there  be  reason  to  suspect  that  the  proper  spe- 
cific gravity  is  not  being  maintained  it  should  be  measured  with 
i  hydrometer.     Fresh  sulfuric  acid  may  be  added  if  one  follows 
carefully  the  specifications  given  by  the  manufacturer  of  the  cell, 
'n  making  fresh  solution  only  sulfuric  acid  free  from  metals  other 
han  lead,  free  from  arsenic,  and  free  from  chloride  and   nitrate 
hould  be  used.     There  will  be  a  continuous  loss  of  water  from  the 
>attery  liquid  due  to  evaporation  and  gassing.     This  should  be 
eplaced  by  distilled  water  during  the  recharging  of  the  cell. 

In  discharging  a  cell  its  voltage  should  not  be  allowed  to  fall 
1  elow  1.8  volts.     When  a  cell  has  reached  this  voltage  it  should  be 


226         THE  DETERMINATION  OF  HYDROGEN  IONS 

recharged  immediately.  If  however  the  cell  has  been  discharged 
to  a  lower  voltage  it  should  be  recharged  at  half  rate. 

In  using  a  storage  cell  to  supply  potentiometer  current  it  is  es- 
sential that  the  highest  stability  in  the  current  should  be  attained 
since  the  fundamental  principle  of  the  potentiometer  involves  the 
maintenance  of  constant  current  between  the  moment  at  which 
the  Weston  cell  is  balanced  and  the  moment  at  which  the  measured 
E.  M.  F.  is  balanced.  Steadiness  of  current  is  attained  first  by 
having  a  storage  cell  of  sufficient  capacity,  and  second  by  using  it 
at  the  most  favorable  voltage.  Capacity  is  attained  by  the  num- 
ber and  size  of  the  plates.  A  cell  of  60  ampere-hour  capacity  is 
sufficient  for  ordinary  work.  The  current  from  a  storage  cell  is 
steadiest  when  the  voltage  has  fallen  to  2  volts.  When  a  potenti- 
ometer system  of  sufficient  resistance  is  used  it  is  good  practice  to 
leave  the  cell  in  circuit,  replacing  it  or  recharging  it  of  course  when 
the  voltage  has  fallen  to  1.8  or  1.9  volts,  and  thus  insure  the  at- 
tainment of  a  steady  current  when  measurements  are  to  be  made. 

In  no  case  should  a  cell  used  for  supplying  potentiometer  cur- 
rent be  wired  so  that  a  throw  of  a  switch  will  replace  the  discharg- 
ing with  the  charging  circuit.  The  danger  of  leakage  from  the 
high  potential  circuit  is  too  great  a  risk  for  the  slight  convenience. 


CHAPTER  XV 

Hydrogen  Generators,  Wiring,   Shielding,  Temperature 
Control,   Purification  of  Mercury 

Hydrogen  generators.  When  there  is  no  particular  reason  for 
attaining  equilibrium  rapidly  at  the  electrode  a  moderate  supply 
of  hydrogen  will  do.  When,  however,  speed  is  essential,  or 
when  there  are  used  those  immersion  electrodes  which  are  not 
well  guarded  against  access  of  atmospheric  oxygen  an  abundant 
supply  of  hydrogen  is  essential.  Indeed  it  may  be  said  that 
one  of  the  most  frequent  faults  of  the  cruder  equipments  is  the 
failure  to  provide  an  adequate  supply  of  pure  hydrogen  or  the 
failure  to  use  generously  the  available  supply. 

Hydrogen  generated  from  zinc  and  sulfuric  acid  has  been  used 

n  a  number  of  investigations.     If  this  method  be  employed, 

particular  care  should  be  taken  to  eliminate  from  the  generator 

;hose  dead  spaces  which  are  frequently  made  the  more  obvious 

evidence  of  bad  design,  to  have  an  abundant  capacity  with  which 

o  sweep  out  the  gas  spaces  of  cumbersome  absorption  vessels 

.  md  to  properly  purify  the  hydrogen.     To  purify  hydrogen  made 

irom  zinc  and  sulphuric  acid  pass  it  in  succession  through  KOH 

l  olution,  HgCl2  solution,  P2O5,  red-hot,  platinized  asbestos,  and  a 

solution  of  Na2S204  (See  Franzen,  Ber.,  39,  906)  (Henrich,  Ber., 

k  8,  1915,  p.  2006). 

A  very  convenient  supply  of  hydrogen  is  the  commercial, 
( ompressed  gas  in  tanks.  According  to  Moser  (1920)  the  indus- 
t  rial  preparation  varies  but  the  chief  methods  are  the  electrolytic 
1  nd  the  Linde-Cara-Franck  processes.  Of  these  the  first  yields 
t  le  better  product.  Hydrogen  by  the  second  process  contains 
s  tnong  other  impurities,  iron  carbonyl  which  may  be  detected  by 
t  le  yellow  flame  and  the  deposit  of  iron  oxid  formed  when  the 
r  ydrogen  flame  impinges  upon  cold  porcelain.  Moser  found  that 
i'  was  impractical  to  remove  this  iron  carbonyl  and  he  states  that 
h  ydrogen  containing  it  is  unfit  for  laboratory  purposes.  On  the 
0  ;her  hand,  electrolytic  hydrogen  ordinarily  contains  only  traces 
0    air  and  C02  and  is  free  from  arsenic  and  CO.     To  purify  it 

227 


228  THE   DETERMINATION   OF   HYDROGEN   IONS 

pass  the  gas  over  KOH  and  then  through  a  tube  of  red-hot,  platin- 
ized asbestos.  If  it  is  desired  to  dry  the  hydrogen,  use  soda  lime 
or  P2O5,  but  not  H2SO4  which  is  reduced.  If  P20B  is  used  it  should 
be  free  from  P2O3,  i.e.,  distilled  in  a  current  of  hot  dry  air. 

In  purchasing  tank  hydrogen  it  is  well  to  be  on  guard  against 
tanks  which  have  been  used  for  other  gases. 

For  controlling  the  flow  of  gas  from  a  high  pressure  tank  the 
valve  on  the  tank  itself  is  seldom  sufficiently  delicate.  There 
should  be  coupled  to  it  a  delicate  needle  valve,  if  this  can  be 
obtained.  If  not  there  will  be  found  on  the  market  diaphragm 
valves  for  the  reduction  of  the  pressure.  Even  then  there  should 
be  placed  between  the  tank  and  the  electrode  vessel  a  T  tube,  one 
branch  of  which  dips  under  mercury  and  forms  a  safety  valve. 

Having  metal  connections  to  start  with,  it  will  be  found  very 
satisfactory  to  lead  off  with  copper  tubing,  such  as  is  used  for 
automobile  connections  or  specified  as  soft  drawn,  seamless  copper 
tubing  4  mm.  internal  diameter  and  wall  thickness  24  B.  S.  gauge. 
This  can  be  soldered  in  the  flame  of  a  blast  lamp,  using  borax  for 
a  flux,  with  a  silver  solder  composed  of  6.5  parts  copper,  2.0 
parts  zinc  and  11.0  parts  silver.  This  solder  is  described  as  fus- 
ing at  about  983°C.  A  nickel  wire  is  useful  in  spreading  the 
flux  and  solder. 

On  the  whole  electrolytic  generators  are  more  satisfactory  if 
a  direct  current  such  as  that  of  a  lighting  circuit  is  available. 
In  figure  34  is  shown  a  generator  the  body  of  which  is  an  ordinary 
museum  jar.  The  glass  cover  may  be  perforated  by  drilling  with 
a  brass  tube  fed  with  a  mixture  of  carborundum  and  glycerine.  If 
this  mixture  is  kept  in  place  by  a  ring  paraffined  in  position,  and 
the  brass  tube  is  turned  on  a  drill  press  with  intermittent 
contact  of  the  drill  with  the  glass,  the  perforation  may  be  .made 
within  a  few  minutes.  The  electrolyte  used  is  ten  per  cent, 
sodium  hydroxid.  The  electrodes  are  nickel.  To  remove 
the  spatter  of  electrolyte  and  to  protect  the  material  in  the  heater 
the  hydrogen  passes  over  a  layer  of  concentrated  KOH  solution; 
and  to  remove  traces  of  residual  oxygen  the  hydrogen  is  passed 
through  a  heater.  In  the  design  shown  the  gas  passes  through  a 
tungsten  filament  lamp.  Lewis,  Brighton  and  Sebastian  use  a 
heated  platinum  wire.  More  commonly  there  is  used  a  gas-heated 
or  electrically  heated  tube  containing  platinized  asbestos.     In 


HYDROGEN    GENERATORS,    ETC. 


229 


the  author's  design  shown  in  figure  34  the  wiring  is  so  arranged 
that  when  there  is  no  demand  for  hydrogen  the  heater  may  be 
turned  off  at  S2  and  a  lamp  thrown  into  series  with  the  generating 

-    + 
I 


Fig.  34.  An  Electrolytic  Hydrogen  Generator 

circuit  by  switch  Si.  The  generator  then  continues  to  operate 
on  a  low  current  and  sufficient  hydrogen  is  liberated  to  keep  the 
system  free  from  air.  Such  a  generator  can  be  run  continuously 
for  months  at  a  time.     When  in  use  the  generator  carries  about 


230  THE   DETERMINATION    OF   HYDROGEN   IONS 

4.5  amperes.  If  this  current  be  taken  from  a  high  voltage  light- 
ing system  there  must  be  placed  in  series  a  proper  resistance  which 
can  be  either  built  up  by  a  bank  of  lamps  or  constructed  from 
nichrome  wire. 

Since  rubber  connections  are  often  used  in  leading  hydrogen 
it  is  of  interest  to  note  the  following  relative  rates  of  diffusion  of 
gases  through  rubber. 

Gab  Rate 

Nitrogen 1.00 

Air 1.15 

Oxygen 2.56 

Hydrogen 5.50 

Carbon  dioxid 13 .57 

Wiring.  Whenever  a  set-up  is  to  be  made  more  than  an  improv- 
isation it  pays  to  make  a  good  job  of  the  wiring.  A  poor  connec- 
tion may  be  a  source  of  endless  trouble  and  unsystematized  wiring 
may  lead  to  confusion  in  the  comparison  of.  calomel  electrodes 
and  the  application  of  corrections  of  wrong  sign. 

Soldered  connections  or  stout  binding  posts  that  permit  strong 
pressure  without  cutting  of  the  wire  are  preferable  to  any  other 
form  of  contact.  If  for  any  reason  mercury  contacts  are  used 
they  had  best  be  through  platinum  soldered  to  the  copper  lead. 
Copper  wires  led  into  mercury  should  not  take  the  form  of  a 
siphon  else  some  months  after  installation  it  may  be  found  that 
the  mercury  has  been  siphoned  off. 

Thermo-electromotive  forces  are  seldom  large  enough  to  affect 
measurements  of  the  order  of  accuracy  with  which  we  are  now 
concerned  if  care  be  taken  to  make  contacts  so  far  as  possible 
between  copper  and  copper  at  points  subject  to  fluctuations  in 
temperature. 

A  generous  use  of  copper  knife  switches,  can  be  made  to  con- 
tribute to  the  ease  and  certainty  of  check  measurements.  For 
instance  if  there  be  a  battery  of  hydrogen  electrodes  and  a  set  of 
calomel  electrodes,  wires  may  be  led  from  each  to  a  centre  con- 
nection of  single-pole,  double-throw  switches  as  shown  in  figure  35. 
All  the  upper  connections  of  these  switches  are  connected  to  the 
+  pole  of  the  potentiometer's  E.  M.  F.  circuit,  and  all  the  lower 
connections  to  the  —  pole.  By  observing  the  rule  that  no  two 
switches  shall  be  closed  in  the  same  direction,  short-circuiting  of 


HYDROGEN    GENERATORS,    ETC. 


231 


combinations  is  avoided.  The  position  of  a  switch  shows  at  once 
the  sign  of  its  electrode  in  relation  to  any  other  that  may  be  put 
into  liquid  junction.  This  is  a  great  convenience  in  comparing 
calomel  electrodes  where  one  half-cell  may  be  positive  to  another 
and  negative  to  a  third.  Such  a  bank  of  single  pole  switches  per- 
mits the  comparison  of  any  electrode  with  any  other  when  liquid 
junction  is  established;  and,  if  a  leak  occur  in  the  electrical  sys- 
tem the  ability  to  connect  one  wire  at  a  time  with  the  potenti- 
ometer and  galvanometer  often  helps  in  the  tracing  of  the  leak. 


Fig.  35.  Switches  for  Connecting  Half-Cells  with  Potentiometer 

Shielding.  Electrical  leaks  from  surrounding  high  potential  cir- 
cuits are  sometimes  strangely  absent  from  the  most  crude  systems 
and  sometimes  persistently  disconcerting  if  there  is  not  efficient 
shielding.  The  principle  of  shielding  is  based  on  the  following 
considerations.  If  between  two  supposedly  well-insulated  points 
on  a  light  or  heating  circuit,  or  between  one  point  of  such  a  circuit 
and  a  grounding  such  as  a  water  or  drain  pipe,  there  is  a  slight 
flow  of  current,  the  electrical  charges  will  distribute  themselves 
over  the  surface  films  of  moisture  on  wood  and  glass-ware.  At 
two  points  between  which  there  is  a  difference  of  potential  the  wires 
of  the  measured  or  measuring  system  may  pick  up  the  difference  of 
potential  to  the  detriment  of  the  measurement.  If  however  all 
supports  of  the  measured  and  measuring  systems  lie  on  a  good  con- 
ductor such  as  a  sheet  of  metal,  the  electrical  leakage  from  without 


232  THE    DETERMINATION    OP   HYDROGEN   IONS 

will  distribute  itself  over  an  equipotential  surface  and  no  differ- 
ences of  potential  can  be  picked  up.  To  shield  efficiently,  then, 
it  is  necessary  that  all  parts  of  the  system  be  mounted  upon  metal 
that  can  be  brought  into  good  conducting  contact.  In  many  in- 
stances the  complications  of  hydrogen  electrode  apparatus  and 
especially  the  separation  of  potentiometer  from  temperature  bath 
make  a  simple  shielding  impracticable.  Care  must  then  be  taken 
that  all  of  the  separate  parts  are  well  connected.  Tinfoil  winding 
of  wire  in  contact  with  unshielded  points  can  be  soldered  to  stout 
wires  for  connection  to  other  parts  by  dropping  hot  solder  on  the 
well-cleaned  juncture. 

Shielding  should  not  be  considered  as  in  any  way  taking  the 
place  of  good  insulation  of  the  constituent  parts  of  the  measured 
or  measuring  systems. 

For  further  details  in  regard  to  shielding  see  W.  P.  White  (1914). 

Temperature  control  is"  a  matter  where  individual  preference  holds 
sway.  There  are  almost  as  many  modifications  of  various  types 
of  regulators  as  there  are  workers.  Even  in  the  case  of  electrical 
measurements  where  orthodoxy  interdicts  the  use  of  a  water  bath 
it  has  been  said  (Fales  and  Vosburgh)  that  it  can  be  made  to  give 
satisfaction. 

Yet  there  are  a  few  who  may  actually  make  use  of  a  few  words  of 
suggestion  regarding  temperature  control  for  hydrogen  electrode 
work. 

As  a  rule  the  water  bath  is  not  used  because  of  the  difficulty  of 
preventing  electrical  leakage.  Some  special  grades  of  kerosene  are 
sold  to  replace  the  water  of  an  ordinary  liquid  bath  but  for  most 
purposes  ordinary  kerosene  does  very  well.  The  free  acid  some- 
times found  in  ordinary  kerosene  may  injure  fine  metallic  instru- 
ments. To  avoid  this  use  the  grade  sold  as  "  acid-free,  medium, 
government  oil." 

A  liquid  bath  has  the  advantage  that  the  relatively  high  spe- 
cific heat  of  the  liquid  facilitates  heat  exchange  and  brings  material 
rapidly  to  the  controlled  temperature,  but  compared  with  an  air 
bath  it  has  the  disadvantage  that  stopcocks  must  be  brought  up  out 
of  the  liquid  to  prevent  the  seepage  of  the  oil.  The  advantage  of 
the  high  specific  heat  of  a  liquid  is  falsely  applied  when  the  con- 
stancy of  a  liquid  bath  is  considered  to  be  a  great  advantage  over 
the  more  inconstant  air  bath.     The  lower  the  specific  heat  of  the 


HYDROGEN    GENERATORS,    ETC.  233 

fluid  the  less  effect  will  variation  in  the  temperature  of  that  fluid 
have  upon  material  which  it  is  desired  to  keep  at  constant  tem- 
perature. For  this  reason  a  well-stirred  air  bath  whose  tempera- 
ture may  oscillate  about  a  well-controlled  mean  may  actually 
maintain  a  steadier  temperature  in  the  material  under  observa- 
tion than  does  a  liquid  bath  which  itself  is  more  constant.  It  is 
the  temperature  of  the  material  under  observation  and  not  the 
temperature  of  the  bath  which  is  of  prime  interest. 

An  air  bath  can  be  made  to  give  very  good  temperature  control 
and  since  it  is  more  cleanly  than  an  oil  bath  and  permits  direct- 
ness and  simplicity  in  the  design  of  apparatus  a  brief  description 
of  one  form  used  by  the  writer  for  some  years  may  be  of  interest. 

A  schematic  longitudinal  section  illustrating  the  main  features 
is  shown  in  figure  36. 

The  walls  of  the  box  are  lined  with  cork  board  finished  off  on 
the  interior  with  "compo  board."  The  front  is  a  hinged  door 
constructed  like  the  rest  of  the  box  but  provided  with  a  double 
glass  window  and  three  4-inch  hand  holes  through  which  appara- 
tus can  be  reached.  On  the  interior  are  mounted  the  two  shelves 
A  and  B  extending  from  the  front  to  the  back  wall  and  providing 
two  flues  for  the  air  currents  generated  by  the  fan  F. 

The  writer  at  one  time  used  a  no.  0  Sirocco  fan  manufactured 
by  the  American  Blower  Company,  demounted  from  its  casing 
and  mounted  in  the  bearing  illustrated.  He  now  uses  a  four- 
blade  fan  taken  from  a  desk-fan  and  mounted  so  that  it  turns 
in  the  hole  F  of  the  partition  and  blows  toward  E.  The  baffle 
plates  at  E,  made  of  strips  of  tin  arranged  as  in  an  egg-box, 
and  intended  to  establish  parallel  lines  of  flow  when  the  centri- 
fugal fan  was  used,  are  now  eliminated. 

In  the  illustration  the  oil  cup  is  shown  as  if  it  delivers  into  an 
annular  space  cut  out  of  the  Babbit-metal  bearing.  In  reality 
this  annular  space  is  provided  by  cutting  away  a  portion  of  the 
steel  shaft. 

The  heating  of  the  air  is  done  electrically  with  the  use  of  bare, 
aichrome  wire  of  no.  30  B.  and  S.  gauge.  When  using  the  centrif- 
ugal fan  the  wire  is  strung  between  rings  of  absestos  board  (the 
'lard  variety  known  as  "transite"  or  "  asbestos  wood")  which  fit 
:>ver  the  fan  at  H.  With  the  blade-fan  the  partition  at  F  is  made 
)f  asbestos  board  and  the  wire  is  strung  over  the  opening.     The 


234 


THE  DETERMINATION  OF  HYDROGEN  IONS 


air  is  thus  heated  at  its  position  of  highest  velocity.  The  elec- 
trical current  in  this  heating  coil  can  be  adjusted  with  the  weather 
so  that  the  time  during  which  the  regulator  leaves  the  heat  on  is 
about  as  long  as  the  time  during  which  the  regulator  leaves  the 
heat  off.  In  other  words  adjustment  is  made  so  that  the  heating 
and  cooling  curves  have  about  the  same  slope,  or  so  that  the  heat- 
ing balances  the  loss  of  heat  through  the  walls. 


1      FOOT 


t- i — r—\ — i — i    i    i    i    i 


— *—" 

-:— \ 

J 

E 

.^ 

Fig.  36.  Cross  Section  of  an  Air  Bath 

When  the  room  temperature  is  not  low  enough  to  provide  the 
necessary  cooling  the  box  I  is  filled  with  ice  water.  Surrounding 
this  is  an  air  chamber  into  which  air  is  forced  from  the  high  pres- 
sure side  of  the  fan.  J  should  be  provided  with  a  damper  which 
can  easily  be  reached  and  adjusted. 

To  lessen  danger  of  electrical  leakage  over  damp  surfaces  the 
air  is  kept  dry  by  a  pan  of  calcium  chlorid. 

A  double  window  at  W  over  which  is  hung  an  electric  light  pro- 
vides illumination  of  the  interior.  A  solution  of  a  nickel  salt  is 
placed  at  this  window  to  absorb  the  heat  from  the  lamp. 


HYDROGEN    GENERATORS,    ETC.  235 

The  double  window  in  the  door  (not  shown)  should  be  beveled 
toward  the  interior  to  widen  the  range  of  vision. 

Such  a  box  has  been  held  for  a  period  of  eight  hours  with  no 
change  which  could  be  detected  by  means  of  a  tapped  Beckmann 
thermometer  and  with  momentary  fluctuations  of  0.003°  as  de- 
termined with  a  thermo-element.  The  average  operation  is  a 
temperature  control  within  ±0.03°  with  occasional  unexplained 
variations  which  may  reach  0.1°.  Because  of  the  slowness  with 
which  air  brings  material  to  its  temperature  the  air  bath  is  con- 
tinuously kept  in  operation,  and  if  a  measurement  is  to  be  made 
quickly  the  solution  is  preheated. 

Given  efficient  stirring  and  a  considerate  regulation  of  the 
current  used  in  heating,  accurate  temperature  control  reduces  to 
the  careful  construction  of  the  regulator.  For  an  air  bath  the 
ideal  regulator  should  respond  instantaneously.  This  implies 
rapid  heat  conduction.  Regulators  which  provide  this  by  having 
a  metal  container  have  been  described  but  glass  will  ordinarily  be 
used.  At  all  events  there  are  two  simple  principles  of  regulator 
construction  the  neglect  of  which  may  cause  trouble  or  decrease 
sensitivity  and  attention  to  which  improves  greatly  almost  any 
type.  The  first  is  the  protection  of  the  mercury  contact  from  the 
corroding  effect  of  oxygen.  The  second  is  the  elimination  of  plati- 
num contacts  which  mercury  will  sooner  or  later  "wet,"  and  the 
substitution  of  an  iron,  nickel  or  nichrome  wire  contact. 

After  trials  of  various  designs  the  author  has  adopted  the  two 
forms  of  regulator  head  shown  in  figure  37. 

For  precise  control  at  an  inaccurately  adjusted  temperature 
form  A  is  used.  The  platinum  lead-in  wire  P  is  fused  to  the  ni- 
chrome wire  N.  After  filling  the  instrument  with  mercury,  dry 
hydrogen  is  flushed  through  the  head  by  way  of  the  side  tubes. 
These  are  then  sealed  off  and  serve  as  reservoirs  for  excess  mer- 
cury. Adjustment  is  made  by  slightly  overheating  the  body  of 
the  mercury,  breaking  off  the  capillary  column  by  a  tap  of  the 
hand  and  storing  the  detached  portion  in  one  of  the  side  tubes. 
Such  an  adjustment  is  often  troublesome  when  regulation  at  a 
particular  temperature  is  desired;  but,  once  the  adjustment  is  made 
it  is  permanent,  provided  the  contact  wire  is  ground  down  to  a 
fine  thread  so  that  it  will  not  fill  the  capillary  enough  to  cause  the 
mercury  thread  to  part  on  occasions  of  overheating. 


236 


THE  DETERMINATION  OF  HYDROGEN  IONS 


Form  B  permits  delicate  adjustment  of  the  contact  by  means  of 
the  screw  S  but  it  requires  skill  to  make  such  a  head  properly. 
The  nichrome  wire  must  fit  very  closely  in  the  capillary  R  to  pre- 
vent the  wax  and  mercury  seal  at  W  from  creeping  downward. 
Such  a  close  fit  implies  very  careful  glass  blowing  to  maintain  a 


Fig.  37.  Thermo-Regtjlator  Heads 

straight  and  unconstricted  capillary.  With  the  contact  wire  in 
place  and  the  proper  amount  of  mercury  in  the  apparatus  hydrogen 
is  run  in  at  T  escaping  through  R.  Then  a  bit  of  beeswax  is 
melted  about  W  and  at  the  moment  it  hardens  the  hydrogen  sup- 
ply is  shut  off,  T  is  sealed,  and  then  the  wax  is  covered  with  a 
shallow  layer  of  mercury. 


HYDROGEN   GENERATORS,    ETC.  237 

If  the  wire  does  not  fit  R  with  precision  or  if  overheating  occurs 
the  mercury  at  W  may  find  its  way  into  the  regulator  head.  It 
is  much  safer  then,  although  it  increases  the  difficulties  of  adjust- 
ment, to  make  the  seal  at  W  with  DeKhotinsky  cement. 

For  an  air  bath  it  is  best  to  seal  such  regulator  heads  to  a 
grid  of  tubes. 

The  permanency  of  regulators  of  such  design  when  properly 
made  is  a  great  asset  and  well  repays  care  in  preparation.  Regu- 
lators of  each  of  these  types  have  been  in  continuous  operation  for 
years  without  serious  trouble.  One  of  type  A  survived  a  severe 
laboratory    fire   and   after   readjustment   operated   well. 

Filling  such  regulators  with  mercury  can  be  done  most  easily 
by  first  evacuating  the  vessel  under  some  one  of  the  various  high 
vacuum  pumps  and  then  letting  the  mercury  in  slowly  through  one 
of  the  side  arms  drawn  to  a  fine  point  which  is.  broken  under 
mercury. 

A  description  of  methods  of  purifying  mercury  will  be  found  on 
page  239. 

For  electrical  control  of  temperature  the  scheme  of  wiring 
shown  in  figure  38  has  proved  satisfactory. 

Lamps  which  are  neat,  convenient,  replacable  forms  of  resist- 
ance, which  are  obtainable  in  variety  and  which  indicate  whether 
or  not  current  is  flowing  are  shown  in  figure  38  "by  L.  R  is  a 
resistance  formed  by  a  few  turns  of  number  30  nichrome  wire  on 
Pyrex  glass,  porcelain  or  asbestos  board.  By  shifting  the  brass 
contact  clamp  along  this  resistance  the  proper  amount  of  cur- 
rent to  operate  the  relay  may  be  found  by  trial.  Too  strong  a 
current  is  to  be  avoided.  A  sharp,  positive  action  of  the  relay 
should  be  provided  against  the  day  when  the  relay  contact  may 
become  clogged  with  dust.  To  reduce  sparking  at  the  regulator 
and  at  the  relay  contacts,  inductive  coils  in  the  wiring  should  be 
avoided.  Spanning  the  spark  gaps  with  properly  adjusted  con- 
densers made  of  alternate  layers  of  tin  foil  and  paraffine  paper 
may  eliminate  most  of  the  sparking,  if  the  proper  capacity  be 
used.  For  air  regulation  it  is  essential  that  the  heater  be  of 
bare  wire  so  that  it  cools  the  moment  the  current  is  turned  off. 
Furthermore  it  is  essential  to  adjust  the  current  till  the  heating 
rate  is  close  to  the  cooling  rate  of  the  air  bath.  For  such  control 
of  the  heating  current  there  are  inserted  in  series  with  the  heater 


238 


THE  DETERMINATION  OF  HYDROGEN  IONS 


two  lamp  sockets  in  parallel  permitting  the  insertion  of  either  a 
fuse,  one  lamp  or  two  lamps  of  various  sizes.  The  other  lamp 
shown  in  the  heating  circuit  reduces  sparking  at  the  relay. 

For  relay  contacts  the  tungsten  contacts  used  in  gas  engines 
are  very  good. 

Although  methods  of  tapping  an  alternating  current  for  the 
operation  of  a  relay  have  been  described  it  is  safer  to  depend  upon 
a  battery. 


To 
VUa-YtY 


Fig.  38.  Wibing  for  Temperature  Control 

Purification  of  mercury.  Pure  mercury  is  essential  for  many 
purposes  in  hydrogen  electrode  work, — for  the  calomel  and  the 
mercury  of  calomel  electrodes,  for  Weston  cells  should  these  be 
"home  made,"  for  thermo-regulators  and  for  the  capillary  elec- 
trometer. 

The  more  commonly  practiced  methods  of  purification  make  use 
of  the  wide  difference  between  mercury  and  its  more  troublesome 
impurities  in  what  may  be  descriptively  put  as  the  "electrolytic 
solution  tension."  Exposed  to  any  solution  which  tends  to  dis- 
solve base  metals  the  mercury  will  give  up  its  basic  impurities 


HYDROGEN    GENERATORS,    ETC.  239 

before  it  goes  into  solution  itself,  provided  of  course  the  reaction 
is  not  too  violent  for  the  holding  of  equilibrium  conditions. 

The  most  commonly  used  solvent  for  this  purpose  is  slightly 
diluted  nitric  acid'  although  a  variety  of  other  solutions  such  as 
that  of  ferric  iron  may  be  used. 

To  make  such  operations  efficient  it  is  necessary  to  expose  as 
large  a  surface  as  possible  to  the  solution.  Therefore  the  mercury 
is  sometimes  sprayed  into  a  long  column  of  solution  which  is  sup- 
ported by  a  narrow  U-tube  of  mercury.  The  mercury  as  it  col- 
lects in  this  U-tube  separates  from  the  solution  and  runs  out  into 
a  receiver.  To  insure  good  separation  the  collecting  tube  should 
be  widened  where  the  mercury  collects  but  this  widening  should 
not  be  so  large  as  to  prevent  circulation  of  all  the  mercury.  A 
piece  of  very  fine-meshed  silk  tied  over  the  widened  tip  of  a  funnel 
makes  a  fine  spray  if  the  silk  be  kept  under  the  liquid.  This  sim- 
ple device  can  be  made  free  from  dead  spaces  so  that  all  the  mer- 
cury will  pass  through  successive  treatments.  It  is  more  difficult 
to  eliminate  these  dead  spaces  in  elaborate  apparatus;  but  such 
apparatus,  in  which  use  is  made  of  an  air  lift  for  circulating  the 
mercury,  makes  practicable  a  large  number  of  treatments.  A 
combination  of  the  air  lift  with  other  processes  and. a  review  of 
similar  methods  has  been  described  by  Patten  and  Mains  (1917). 

Hulett's  (1905,  1911)  method  for  the  purification  of  mercury 
consists  in  distilling  the  mercury  under  diminished  pressure  in  a 
current  of  air,  the  air  oxidizing  the  base' metals.  Any  of  these 
oxids  which  are  carried  over  are  filtered  from  the  mercury  by  pass- 
ing it  through  a  series  of  perforated  filter  papers  or  long  fine  cap- 
illaries. A  convenient  still  for  the  purpose  is  made  as  follows. 
Fuse  to  the  neck  of  a  Pyrex  Kjeldahl  flask  a  tube  about  30cm.  long 
which  raises  out  of  the  heat  of  the  furnace  the  stopper  that  car- 
ries the  capillary  air-feed.  Into  the  neck  of  the  flask  fuse  by  a  T- 
joint  seal  a  1.5  cm.  tube  and  bend  this  slightly  upward  for  a 
length  of  15  cm.  so  that  spattered  mercury  may  run  back.  To  the 
end  of  this  15  cm.  length  join  the  condensing  tube,  which  is  simply 
an  air  condenser  made  of  a  meter  length  of  narrow  tubing  bent 
zigzag.  Pass  the  end  of  this  through  the  stopper  of  a  suc- 
tion flask  and  attach  suction  to  the  side  tube  of  this  flask.  The 
mercury  in  the  Kjeldahl  flask  may  be  heated  by  a  gas  flame  or  an 
electric  furnace.     For  a  220  volt  D.  C.  circuit  12  meters  of  no.  26 


240         THE  DETERMINATION  OF  HYDROGEN  IONS 

nichrome  wire  wound  around  a  thin  asbestos  covering  of  a  tin 
can  makes  a  good  improvised  heating  unit  if  well  insulated  with 
asbestos  or  alundum  cement.  A  little  of  this  cement  applied 
between  the  turns  of  wire  after  winding  will  keep  the  wire  in  place 
after  the  expansion  by  the  heat. 

In  the  construction  of  such  stills  it  is  best  to  avoid  soft  glass 
because  of  the  danger  of  collapse  on  accidental  over-heating. 
Hostetter  and  Sosman  describe  a  quartz  still. 

Both  the  air  current,  that  is  delivered  under  the  surface  of  the 
mercury  by  means  of  a  capillary  tube,  and  the  heating  should  be 
regulated  so  that  distillation  takes  place  smoothly. 

Since  it  is  very  difficult  to  remove  the  last  traces  of  oxid  from 
mercury  prepared  by  Hulett's  distillation  the  author  always  makes 
a  final  distillation  in  vacuo  at  low  temperature.  An  old  but  good 
form  of  vacuum  still  is  easily  constructed  by  dropping  from  the 
ends  of  an  inclined  tube  two  capillary  tubes  somewhat  over  baro- 
metric length.  One  of  these  is  turned  up  to  join  a  mercury  res- 
ervoir, the  other,  the  condenser  and  delivery  tube,  is  turned  up 
about  4  inches  to  prevent  loss  of  the  mercury  column  with  changes 
in  external  pressure.  The  apparatus  is  filled  with  mercury  by  suc- 
tion while  it  is  inclined  to  the  vertical.  Releasing  the  suction  and 
bringing  the  still  to  the  vertical  leaves  the  mercury  in  the  still 
chamber  supported  by  a  column  of  mercury  resting  on  atmospheric 
pressure  and  protected  by  the  column  in  the  capillary  condenser. 
The  heating  unit  is  wire  wound  over  asbestos.  The  heat  should 
be  regulated  by  a  rheostat  till  the  mercury  distills  very  slowly. 
By  having  the  mercury  condense  in  a  capillary  the  still  becomes 
self-pumping. 

Perhaps  few  of  us  who  work  with  mercury  have  a  proper  regard 
for  the  real  sources  of  danger  to  health.  The  vapor  pressure  of 
mercury  at  laboratory  temperatures  is  not  to  be  feared,  but  emul- 
sification  with  the  dust  of  the  floor  may  subdivide  the  mercury 
until  it  can  float  in  the  air  as  a  distinct  menace.  Its  handling 
with  fingers  greasy  with  stop  cock  lubricant  is  also  to  be  avoided 
on  account  of  possible  penetration  of  the  skin  but  more  particu- 
larly because  of  the  demonstrated  ease  with  which  material  on 
the  hands  reaches  the  mouth. 


HYDROGEN  GENERATORS,  ETC.  241 

REFERENCES 

Potentiometers 

Bartell  (1917),  Bovie  (1915),  Hildebrand  (1913),  Leeds  and  Northrup  Cata- 
logue 70,  McClendon  (1915),  Nye  (1921),  Sand-Law  (1911),  Slagle- 
Acree  (1921),  Wenner-Weibel  (1914),  White  (1914),  Will  Corporation 
(1921). 

Galvanometers 

Leeds  and  Northrup  Company  Catalogue  20  (1918),  White  (1906). 

Capillary   electrometer 

Boley  (1902),  Le  Blanc  (1890),  Lippmann,  G.  (1875),  Smith  (1900)  (1903). 

Quadrant  electrometer 

Beattie  (1910-12),  Compton-Compton  (1919),  Dolezalek  (1906). 

Weston  standard  cell 

Bureau  Standards  Circular  60,  Report  to  International  Committee  (1912), 
Cohen-Moesveld  (1920),  Cohen-Walters  (1920),  Wolff  (1908),  Wolff- 
Waters  (1907),  Hulett  (1906),  Melon  (1921),  Oblata  (1920). 

International  electrical  units 
Dellinger  (1916),  Bureau  Standards  Circulars  Nos.  29,  60. 


CHAPTER  XVI 

The  Relation  of  Hydrogen  Electrode  Potentials  to 
Reduction  Potentials 

We  must  remember  that  we  cannot  get  more  out  of  the  mathematical 
mill  than  we  put  into  it,  though  we  may  get  it  in  a  form  infinitely  more 
useful  for  our  purpose. — John  Hopkinson 

As  indicated  in  Chapter  X  the  hydrogen  electrode  is  but  a 
special  case  of  a  general  relation  for  the  potential  difference  be- 
tween a  metal  and  a  solution.  The  hydrogen  electrode  is  con- 
structed of  a  noble  metal  laden  with  hydrogen,  and  it  may  be 
asked  what  relation  it  bears  to  those  electrodes  which  consist  of 
the  noble  metal  alone  and  which  are  used  to  determine  the  so- 
called  oxidation-reduction  potentials  of  solutions  such  as  mix- 
tures of  ferrous  and  ferric  iron. 

If  a  platinum  or  gold  electrode  be  placed  in  a  mixture  of  fer- 
rous and  ferric  sulfate  there  will  almost  immediately  be  assumed 
a  stable  potential  difference  which  is  determined  by  the  ratio 
of  the  ferrous  to  the  ferric  ions.  The  relation  which  is  found  to 
hold  is  given  by  the  equation: 

fc-fc-MfcEsd  (44) 

nF       [Fern] 

where  Eh  is  the  observed  potential  difference  between  the  elec- 
trode and  the  standard  normal  hydrogen  electrode,  E^  is  a  con- 
stant characteristic  of  this  particular  oxidation-reduction  equilib- 

[Ferro] 
rium  and  equal  to  Eh  when  the  ratio  — — jj  is  unity,  R,  T,  n 

and  F  have  their  customary  significances,  and  [Ferroj  and  [Ferri] 
represent  concentrations  of  the  ferrous  and  the  ferric  ions  re- 
spectively. This  equation  will  be  referred  to  later  as  Peters' 
equation.     Its  general  form  is: 

RT,    [RED]  ,    % 

where  [RED]  represents  the  concentration  of  the  reductant  and 
[OX]  represents  the  concentration  of  the  oxidant. 

242 


REDUCTION    POTENTIALS  243 

If  we  plot  Eh  on  one  coordinate  and  the  percentage  reduction 
on  the  other  coordinate,  we  obtain  a  set  of  curves  identical  in 
form  for  a  given  value  of  n.  The  position  of  each  curve  along 
the  Eh  axis  is  determined  by  the  value  of  Ek  which  fixes  the  middle 
point.  Such  a  set  of  curves  would  present  a  picture  comparable 
with  that  shown  in  figure  2.  The  picture,  however,  would  be 
incomplete  for  reasons  which  will  be  given  later. 

It  will  be  clearly  understood  that  in  using  the  term  oxidation 
or  the  term  oxidant  we  do  not  imply  that  oxygen  is  concerned. 
Oxidation  is  one  of  those  terms  established  under  an  old  order 
of  thought  and  carried  on  into  a  new  order  with  its  meaning 
broadened.  In  the  transformation  of  ferrous  to  ferric  iron  by 
chlorine  there  is  every  reason  to  believe  that  the  process  is  directly 
one  of  electron  transfer;  yet  we  speak  of  it  as  an  "oxidation" 
because  it  was  seen  fit  at  one  time  to  systematize  such  reactions 
in  terms  of  the  participation  of  oxygen.  The  counterpart  of 
oxidation  is  reduction.  This  term  does  not  directly  indicate  any 
relation  to  hydrogen,  but  it  is  often  assumed  that  hydrogen  is 
concerned  in  reduction  in  much  the  same  way  that  oxygen  was 
thought  to  be  concerned  in  every  "oxidation." 

Before  coming  to  a  more  generalized  theory  we  shall  describe 
the  relation  between  the  hydrogen  electrode  and  the  oxidation- 
reduction  electrode  in  terms  of  hydrogen  and  hydrogen  ions.    . 

It  is  known  that  certain  reducing  agents  are  so  active  that 
they  evolve  hydrogen  from  aqueous  solutions.  In  such  a  solu- 
tion an  electrode  would  become  charged  with  hydrogen  and 
would  conduct  itself  much  like  a  hydrogen  electrode.  The  relations 
then  obtaining  can  be  extended  and,  if  we  wish  to  represent  the 
interaction  of  the  reducing  agent  with  the  hydrogen  ions,  we  have: 

H+  +  reducing  agent  ^  H  +  oxidation  product. 

If  equilibrium  is  established  for  the  above  reaction 

[H+]  [RED]  = 
[H]  [OX] 

[H]  _  [RED] 

FH+]       [OX] 


244  THE    DETERMINATION    OF   HYDROGEN   IONS 

[H]  [RED] 

Substituting  K  zz^;,  for  the  ratio  "77^77  in  Peters'  equation 

(45)  and  placing  n  =  1  for  the  case  at  hand  we  have 

Since  the  atomic  hydrogen  bears  a  definite  relation  to  the  partial 
pressure  of  molecular  hydrogen,  P,  through  the  equilibrium 

[Hj2  =  KhP 

we  mav  substitute,  collect  constants  under  another  constant  K', 
bring  this  under  Ek  and  so  obtain: 

-       „,       RT.    \/~P~  ,    N 

Eh  =  Ek  -  —  In  _  .(46) 

Compare  this  with  the  general  relation  for  the  hydrogen  electrode 

„        „        RT.    V^P~  ,    % 

Eh  =  EH In  — —  (47) 

F  [H+] 

EH  in  (47)  is  zero  by  definition  when  there  is  used  the  "normal 
hydrogen  electrode"  system  of  reference.  When  (46)  is  placed 
on  .the  same  basis  Ek  is  also  zero,  since  each  of  the  other  terms  in 

(46)  is  identical  with  the  corresponding  term  in  (47). 

In  other  words  we  have  substituted  for  the  oxidation-reduction 
equilibrium  the  corresponding  point  of  equilibrium  between 
hydrogen  and  hydrogen  ions,  and  have  considered  the  poten- 
tial difference  at  the  electrode  as  if  it  were  that  of  a  hydrogen 
electrode.  An  inference  is  that  wherever  we  have  an  oxidation- 
reduction  equilibrium  the  components  will  interact  with  hydrogen 
ions  (or  water)  liberating  free  hydrogen  and  building  up  in  the 
electrode  a  definite  pressure  of  hydrogen.  Conversely,  if  hydro- 
gen is  already  present  in  the  electrode  at  a  pressure  too  high  for 
the  oxidation-reduction  equilibrium  in  question,  hydrogen  will 
be  withdrawn  until  its  pressure  is  in  harmony  with  the  oxidation- 
reduction  equilibrium  (the  position  of  the  latter  having  been 
shifted  more  or  less  by  the  reduction) .  When  a  constant  pressure 
of  hydrogen  is  maintained  at  the  electrode,  as  it  is  in  the  customary 
use  of  the  hydrogen  electrode,  no  true  equilibrium  can  be  attained 


REDUCTION   POTENTIALS  245 

until  this  hydrogen  has  so  far  reduced  all  the  substances  in 
the  solution  that  they  can  support  one  atmosphere  pressure  of 
hvdrogen. 

Incidentally  it  may  be  mentioned  that  it  is  a  matter  of  indiffer- 
ence whether  we  regard  the  reductant  to  interact  with  the  hydro- 
gen ions  or  the  oxidant  with  the  hydroxyl  ions  or  each  with  water. 
By  use  of  the  equilibrium  equations  which  are  involved  we  reach 
the  same  end-result  whatever  the  path.  And  furthermore  by 
the  use  of  certain  theoretical  relations  between  the  hydrogen  elec- 
trode and  the  oxygen  electrode  we  could  define  potential  differences 
in  terms  of  that  of  an  oxygen  electrode. 

This  method  of  relating  oxidation-reduction  to  electrode  poten- 
tials is  convenient  for  showing  the  condition  which  must  obtain  for 
a  true  hydrogen  electrode  potential;  but  when  we  attempt  to 
follow  some  of  the  logical  consequences  of  this,  the  customary 
exposition,  we  not  only  meet  some  serious  difficulties  but  obscure 
some  very  important  relations. 

Let  us  calculate  the  hydrogen  pressure  in  equilibrium  with  an 
equimolecular  mixture  of  ferrous  and  ferric  chlorid  in  a  solution 
held  at  pH  1.  A  platinum  electrode  in  such  a  solution  will  have 
a  potential  about  0.75  volt  more  positive  than  the  "normal  hy- 
drogen electrode."  Let  us  consider  this  to  be  the  difference  of 
potential  between  a  hydrogen  electrode  at  pH  1  and  a  normal 
hydrogen  electrode.  Let  us  calculate,  then,  the  hydrogen  pressure 
at  25°C.  from  the  equation: 

0.75  =  -  0.0599  log  — 
0.1 

We  find  the  hydrogen  pressure  to  be  about  10~27  atmospheres. 
At  one  atmosphere  pressure  a  gram  mol  of  hydrogen  occupies 
about  22  litres  and  contains  about  6  X  1023  molecules.  If  the 
pressure  is  reduced  to  6  X  10-23  atmospheres  there  would  be  but 
one  molecule  of  hydrogen  in  22  litres.  If  reduced  to  10-27  at- 
mospheres there  would  be  but  one  molecule  in  about  37,000  litres. 
To  assume  any  physical  significance  in  such  values  is,  of  course, 
ridiculous. 

It  is  only  by  courtesy  then  that  an  electrode  in  a  mixture  of 
ferrous  and  ferric  iron  at  pH  1  can  be  considered  as  a  hydrogen 
electrode. 


246  THE   DETERMINATION    OF   HYDROGEN   IONS 

This  is  but  an  instance  of  the  physically  absurd  values  encoun- 
tered when  restricted  points  of  view  and  restricted  methods  of  expressing 
relations  are  applied  to  electrode  potential  differences.  One  or  two 
other  instances  will  be  given  to  illustrate  the  fact  that  our 
present  equations  are  incomplete  in  that  they  tell  us  little  or 
nothing  about  the  mechanisms  at  electrodes  (see  Langmuir  1916, 
also  Smits  and  Aten  1916). 

Lehfeldt  (1899)  says  of  the  so-called  solution  pressures  postu- 
lated by  Nernst  and  briefly  discussed  in  Chapter  X: 

we  have  Zinc 9.9  X  1018 

Nickel 1.3  X  10° 

Palladium 1.5  X  10~36 

The  first  of  them  is  startlingly  large.  The  third  is  so  small  as  to  involve 
the  rejection  of  the  entire  molecular  theory  of  fluids. 

Lehfeldt  then  shows  that,  in  order  to  permit  at  the  electrode 
the  pressure  indicated  above  for  palladium,  the  solution  would 
have  to  be  so  dilute  as  to  contain  but  one  or  two  ions  of  palladium 
in  a  space  the  size  of  the  earth.  No  stable  equiHbrium  could  be 
measured  under  such  a  circumstance.  On  the  other  hand  Leh- 
feldt calculates  that  to  produce  the  high  pressure  indicated  for 
zinc  "1.27  grams  of  the  metal  would  have  to  pass  into  the  ionic 
form  per  square  centimeter,  which  is  obviously  not  the  case." 
There  is  thus  very  good  reason  to  refrain  from  attributing  a  limited 
and  sometimes  obviously  untrue  physical  significance  to  the  in- 
tegration constant  in  the  fundamental  equation  for  electrode 
potentials  (see  page  153). 

Another  aspect  of  the  matter  was  emphasized  in  a  lively  dis- 
cussion between  Haber,  Danneel,  Bodlander  and  Abegg  in  Zeit- 
schrift  fur  Elektrochemie,  1904.  Haber  points  out  that,  if  the 
well  established  relation  between  silver  ion  concentration  and  the 
potential  difference  between  a  silver  electrode  and  a  solution 
containing  silver  ions  be  extrapolated  to  include  the  conditions 
found  in  a  silver  cyanide  solution,  the  indicated  concentration  of 
the  silver  ion  will  be  so  low  as  to  have  no  physical  significance. 
Haber  mentions  the  experiment  of  Bodlander  and  Eberlein  where 
the  potential  and  the  quantity  of  solution  were  such  that  there 
was  present  at  any  moment  less  than  one  discrete  silver  ion.  The 
greater  part  of  the  discussion  centred  upon  the  resolution  of  the 
equilibrium  constant  into  a  ratio  of  rates  of  reaction,  and  upon 


REDUCTION    POTENTIALS  247 

the' conclusion  that,  if  the  silver  ion  in  the  cyanide  solution  has  a 
concentration  of  the  order  of  magnitude  calculated,  it  must  react 
with  a  speed  greater  than  that  of  light  or  else  that  the  known  reac- 
tions of  silver  in  cyanide  solutions  must  take  place  partly  with 
the  silver  complexes  and  not  wholly  with  the  silver  ions.  How- 
ever, we  are  now  more  directly  concerned  with  another  aspect  of 
this  interesting  situation.  The  potentials  observed  in  silver  cya- 
nide solutions  are  well  defined.  We  may  choose  to  extend  to 
such  solutions  the  relation  between  the  potential  of  a  silver  elec- 
trode and  silver  ion  concentration.  When  we  do,  we  find  that  the 
silver  ion  concentration  by  itself  cannot  account  for  the  well-de- 
fined potential.  How  then  is  the  stable  and  reproducible  poten- 
tial supported? 

None  of  these  discussions  affect  in  any  serious  way  those  rela- 
tions for  concentration  chains  which  are  founded  upon  thermo- 
dynamic reasoning  provided  it  be  remembered  that  the  thermo- 
dynamic reasoning  alone  does  not  furnish  any  conception  of  the 
physical  mechanisms  of  a  process.  The  points  mentioned  do  how- 
ever make  it  evident  that  values  sometimes  used  are  mere  "cal- 
culation numbers"  employed  in  a  region  of  extrapolation  where 
the  actual  physical  significance  is  unknown.  The  inevitable  con- 
clusion is  that  our  equations  are  insufficiently  generalized. 

Such  "calculation  numbers"  as  those  mentioned  in  the  pre- 
3eding  discussion  are  often  of  very  great  usefulness,  but  lest 
ihey  continue  to  obscure  phenomena  of  significance  we  shall 
soon  have  to  have  equations  more  intimately  related  to  the  mech- 
misms  as  Langmuir  pointed  out  in  his  1916  paper. 

Now  it  will  not  remove  the  fundamental  difficulty  to  use  the 

reatment  which  follows;  but  this  treatment  may  aid  the  student 

o  retain  an  orderly  view  of  important  relations,  and  it  will  pro- 

"  'ide  a  basis  from  which  to  discuss  the  interrelations  of  electrodes 

<f  different  types.     From  this  discussion  a  generalized  point  of 

"  iew  will  be  reached. 

It  is  generally  agreed  that  the  fundamental  process  in  oxida- 
1  on-reduction  is  an  exchange  of  electrons.     A  familiar  example  is: 

Ferric  ion  +  electron  ^=±  ferrous  ion 

Fe+++  +        e        ?±  Fe++ 

Since  such  a  reversible  reaction  is  not  dependent  upon  the 
F  'esence  of  an  electrode  (acting  as  a  catalyst)  it  is  probable  that 


248         THE  DETERMINATION  OF  HYDROGEN  IONS 

an  exchange  of  electrons  is  going  on  continuously.  There  must 
then  be  some  condition  virtually  equivalent  to  a  free-electron 
pressure.  We  may  imagine  a  moment  in  the  exchange  during 
which  the  electron  is  balanced  between  the  forces  of  each  ion. 
At  this  moment  the  electron  may  be  considered  to  belong  to 
neither  ion  and  to  be  a  property  of  the  environment.  Undoubtedly 
the  situation  is  not  so  simple  as  this  picture  suggests;  and,  al- 
though the  presence  of  free  electrons  has  been  demonstrated  in 
liquid  ammonia  and  methylamine  solutions,  the  experimental 
evidence  is  not  sufficient  to  justify  our  assuming  the  presence  of 
free  electrons  in  aqueous  solutions  to  be  a  fact.  However,  it  may 
be  said  at  once  that  we  are  not  now  concerned  with  the  objective 
actuality.  A  pressure  of  free  electrons  is  merely  postulated  as 
the  virtual  equivalent  of  a  condition  not  yet  clearly  formulated; 
and  it  is  to  be  used  in  much  the  same  way  that  Nernst  used  "so- 
lution tension,"  destined  from  the  first  to  be  eliminated  from 
those  equations  which  are  employed  to  formulate  experimental 
data. 

Assuming  then  the  presence  of  free  electrons  as  representative 
of  some  condition  which  may  be  tentatively  evaluated  in  terms  of 
electron  pressure,  electron  concentration,  or  electron  activity, 
let  us  consider  the  electrons  to  obey  the  laws  of  an  ideal  solution, 
their  concentration  thus  being  amenable  to  the  law  of  mass  action. 

Then,  for  the  equilibrium  between  ferrous  and  ferric  ions  we  may 
write 

[Fe+++]  [e] 

~pe^r=KFe 

Let  the  symbol  [RED]  stand  for  the  concentration  of  a  reduc- 
tant  and  [OX]  for  the  concentration  of  the  reductant's  oxidation 
product.  Then,  in  general,  for  the  type  of  reaction  represented 
below  where  n  electrons  are  concerned  we  have  the  equilibrium 
equation  (48) 

OX  +  ne^  RED 

[OX][e]"=K]  (48) 


or 


[RED] 


M-V*^ 


REDUCTION    POTENTIALS  249 

For  the  reaction  2H+  +  2e  ^  H2  the  equilibrium  equation  is 

[H+]2  r*i2 


[H, 


=  KH  (50) 


In  (50)  [H2]  refers  to  the  concentration  of  molecular  hydrogen 
in  solution.  Since  we  shall  deal  with  the  partial  pressure  of 
gaseous  hydrogen,  as  is  the  custom,  we  introduce  [H2]  =  K  P 
where  K  is  the  equilibrium  constant  and  P  is  the  partial  pressure 
of  gaseous  hydrogen  expressed  in  atmospheres.  Collecting  con- 
stants we  have 

[H+Ne]2 


=  KH 


or 


[e]  =  ^K, 


P_ 

[H+]2 


By  the  same  procedure  similar  equations  can  be  developed  for 
any  pair  of  oxidation-reduction  products. 

We  shall  now  introduce  [e]  into  an  equation  formulating  the 
difference  of  potential  between  an  electrode  and  an  aqueous  solu- 
tion with  which  it  is  in  contact. 

We  shall  assume  the  presence  of  free  electrons  in  metals,  as 
is  commonly  done.  We  have  already  postulated  free  electrons 
in  solution  as  the  virtual  equivalent  of  the  ability  of  the  solution 
to  give  up  electrons  to  a  body  brought  into  the  solution.  We 
shall  now  ascribe  to  the  electrons  in  the  metal  phase  and  to  the 
electrons  in  the  solution  phase  activities  £m  and  £s  respectively, 
defining  activity  as  Lewis  has  done  (see  page  278). 

The  change  in  free  energy  accompanying  the  isothermal  trans- 
fer of  one  Faraday  of  electrons  from  one  phase  to  the  other  is 

AF  =  RTln^ 

If  E  is  the  difference  of  potential  between  metal  and  solution  and 
F  the  Faraday,  EF  =   A  F 

Hence :  E  =  — r  In  £m —  In  £s 

r  r 


250  THE    DETERMINATION    OF   HYDROGEN    IONS 

More  rigid  equations  of  the  same  general  form  have  been  used 
by  Herzfeld  (1915,  1918),  Langmuir  (1916),  Smits  and  Aten 
(1916),  and  Reichinstein  (1921)  and  have  been  derived  by  reason- 
ing on  kinetic  as  well  as  on  thermodynamic  theory.  Certain 
aspects  of  the  following  treatment  have  been  developed  more 
fully  by  Smits  and  Aten. 

Now  in  the  above  equation  we  have  used  electron  activity. 
In  order  to  bring  the  further  treatment  into  harmony  with  that 
used  consistently  throughout  this  book,  we  shall  have  to  sacrifice 
a  certain  degree  of  generality  and  shall  imagine  that  we  are 
dealing  with  ver3>-  dilute  solutions  wherein  activity  approaches 
concentration.  The  like  assumption  will  be  made  for  the  activity 
of  the  electrons  in  the  metal.     Then  we  may  write 

E  =  —  In  [e]m  -  —  In  [e],    .  (52) 

where  [e]m  is  the  concentration  of  electrons  in  metal  and  [e]B  the 
concentration  in  the  solution. 

Substitute  for  [e]8  its  equivalent  in  any  one  of  the  equilibrium 
equations  and  we  have  a  result  such  as  that  given  below. 

For  instance,  let  two  hydrogen  electrodes  be  constructed  of 
the  same  metal  so  that  when  these  two  electrodes  'are  opposed 
as  in  a  gas  chain  the  Volta-effect  between  the  electrodes  and  the 
copper  of  the  measuring  system  will  be  compensated.  The 
total  E.  M.  F.  of  the  gas  chain  is: 

VKH 
[H+]2 
E.M.F.  -  —  In  e  m  -  — -  In  [e]m  -+  —  In 
F  F  F 


VKHii& 


If  p  =  P' 


„.-„       RT,     H+' 
E.M.F.  =  - — In ,- — f- 
F       IH+] 

This  is  the  simplest  equation  for  a  hydrogen  electrode  concentra- 
tion cell.  In  a  similar  way  we  obtain  the  equation  for  a  con- 
centration cell  of  two  "reduction  potential"  electrodes. 

It  will  be  noted  that  in  the  case  mentioned  above  the  terms 
containing  [e]m  certainly  cancel  out.     But  will  they  if  for  one  of 


REDUCTION    POTENTIALS  251 

two  like  electrodes  another  of  a  different  metal  is  substituted? 
Whatever  the  arguments  for  and  against  this  may  be,  we  believe 
that  the  electrochemical  experimental  data  are  quite  insufficient  to 
decide  the  question.  Lest  important  phenomena  be  thus  obscured, 
as  Smits  believes,  the  reader  should  be  on  his  guard;  but  lest  it 
be  supposed  that  characteristic  differences  between  different 
metals  are  thus  eliminated  it  may  be  said  at  once  that  these 
differences  will  presently  be  found  to  be  embodied  in  a  complex 
of  constants.  We  shall  tentatively  assume  that  the  concentra- 
tions of  the  electrons  in  different  metals  are  sufficiently  alike 
to  permit  differences  to  be  ignored  for  purposes  of  approximate 

treatment  and  shall  regard  the  term  —  In  [e]m  as  a  constant,  Em. 

r 

We  then  have  a  general  equation  for  the  difference  of  potential 

between  any  electrode  and  a  solution  of  hypothetical  electron 

concentration  [e]s,  namely, 

E  =  Em-^ln[e]s  (53) 

To  obtain  an  expression  relating  the  potential  difference  at 
an  electrode  with  the  equilibria  of  the  ions  in  solution  it  is  now 
only  necessary  to  write  a  given  reaction  in  a  form  involving  elec- 
tron concentration,  to  solve  for  [e]8  and  to  introduce  the  equiva- 
lent of  [e]8  in  equation  (53).  Thus  the  working  equation  is  ob- 
tained by  a  uniform  process,  and,  whatever  the  limitations 
of  the  development  may  be,  it  furnishes  at  one  and  the  same  time 
an  easy  method  of  remembering  electrode  relations  and  a  view- 
point which  helps  to  clarify  the  interrelationships  of  different 
systems. 

Since  it  will  be  convenient  to  refer  all  electrode  potential  differ- 
ences to  that  of  the  normal  hydrogen  electrode  as  the  standard, 
the  nature  of  the  relation  will  be  treated  first. 

Combine  equations  (51)  and  (53)  to  give 


E  =  Em-^lnyKH 


But 


[m 


TD'T'  

——In  vKh  is  a  constant  which  we  may  call  Eh. 


252  THE   DETERMINATION    OF   HYDROGEN   IONS 

Hence 

RT     \/   P 
E  =  Em-EH-^ln^p  (54) 

For  an  oxidation-reduction  electrode  we  have  from  equations 
(49)  and  (53) 

E  =  Em-^lnK1^PJ 
nF  [OX] 

or,  separating  the  new  constant  as  we  have  done  above,  we  have 

_      „         „       RT,    [RED]  ,    N 

E  =  Em_El__lnL__J  (55) 

If  now  a  normal  hydrogen  electrode  and  an  oxidation-reduction 
electrode  be  opposed  in  a  "chain"  we  have  from  (54)  and  (55) 
the  full  equation: 

E.M.F.  =  Em  -  Em  +  EH  -  E>  +  ^ln  ^  -  ^Inl^S 

F         LH+]         nF       [OX] 

By  definition  E  in  equation  (54)  is  zero  when  P  and  [H+]  are 
unity.  Then  Em  —  EH  =  0.  The  above  equation  then  (when 
one  of  the  electrodes  is  the  ".normal  hydrogen  electrode")  re- 
duces to 

E.M.F.  =  Em-El-f,„^g!  («> 

It  will  be  noted  that  the  constant  in  this  equation  (algebraic 
sum  of  Em  and  Ei)  is  not  the  simple  constant  of  the  oxidation- 
reduction  equilibria,  but  is  a  complex.  Furthermore  the  value 
is  dependent  upon  the  standard  of  reference  used — in  this  case 
the  normal  hydrogen  electrode.  The  complex  nature  of  this  con- 
stant has  been  discussed  by  Haber. 

It  is  customary  to  combine  such  constants  as  Em  and  Ei  in  the 
last  equation.  Furthermore  it  is  convenient  to  maintain  the 
same  basis  of  reference,  the  normal  hydrogen  electrode.  When 
this  is  done  it  shall  be  indicated  by  using  for  the  electrode  poten- 
tial the  symbol  Eh. 

With  these  understandings  we  may  at  once  write  equations 
for  several  types  of  electrode-solution  systems. 
For  the  hydrogen  electrode 

Eh  =  _?Tln^4:  (57) 

F  [H+l 


REDUCTION    POTENTIALS  253 

For  the  oxygen  electrode 

RT,    [OH-] 
Eh  =  Ek0-—ln-V-^i  (58) 

b        VP02 
For  an  oxidation-reduction  electrode 

F        v     _RT      [RED]  .    . 

Eh  -  Ekl     ^f  ln  ToxT  (59) 

For  a  metal  electrode  in  contact  with  solution  containing  metal 
ions  of  the  electrode  metal 

RT      _[ML 

nF   n[Mn+] 


Eh=E;-— ln^r  (60) 


Here  [M]8  is  the  hypothetical  concentration  of  metal  in  solution 
supposedly  in  equilibrium  with  the  electrode.  [Mn+]  is  the  con- 
centration of  metal  ions  with  n  positive  charges. 

If  [M],  =  K[M]m,  where  [M]m  is  the  concentration  of  undisso- 
ciated  metal  in  the  electrode  and  K  is  the  equilibrium  constant, 
We    may   substitute    and    collect    constants    thereby  obtaining: 

Eh„r_RTIn[M]m 


nF       [Mn+] 

If  the  particular  metal  is  always  of  the  same  density  and  state, 
and  its  electron  concentration  is  constant  (compare  Smits),  we 
can  regard  [M]m  in  the  above  equation  as  constant  and  so  obtain 
equation  (61)  which  is  customarily  used  to  relate  the  poten- 
tial difference  at  a  given  metal  electrode  to  the  concentration  of 
the  metal  ions  in  the  solution . 

Eh  =  EM  +  ?£  In  [M*+]  (61) 

nF 

The  potentials  of  amalgam  electrodes  may  be  derived  in  a  com- 
parable way. 

In  correlating  all  equilibria  about  the  hypothetical  electron 
concentrations  of  solutions,  and  connecting  each  in  an  electrode 
potential  equation  by  means  of  equation  (53)  there  is  made  evi- 
dent a  definite  interrelationship  of  all  reactions  involving  elec- 
tron transfer.  In  the  elementary  development  given,  rigidity 
has  been  sacrificed  for  the  sake  of  a  simplicity  which  it  is  believed 
represents  relations  with  sufficient  truth  to  indicate  the  following 
important  matters  easily  overlooked. 


254  THE   DETERMINATION    OF   HYDROGEN   IONS 

In  the  first  place  it  is  readily  perceived  that  it  is  a  mere  matter 
of  choice  whether  we  regard  a  given  electrode  to  be  acting  as  an 
"oxidation-reduction  electrode"  or  as  a  hydrogen  electrode; 
and  it  only  requires  extension  of  the  same  principle  to  show  that 
this  same  electrode  can  be  considered  as  a  metal  electrode  in 
equilibrium  with  a  solution  of  its  own  ions.  As  indicated  on 
page  245  a  platinum  electrode  immersed  in  a  solution  of  ferrous 
and  ferfic  ions  if  treated  as  a  hydrogen  electrode,  furnishes  a 
hydrogen  pressure  which  can  be  considered  only  as  a  "calcula- 
tion value."  By  a  similar  procedure  it  can  be  shown  that  the 
estimated  platinum-ion  concentration  would  be  a  mere  "calcula- 
tion value"  so  that  we  naturally  avoid  considering  the  electrode 
in  this  case  as  anything  other  than  a  means  of  picking  up  elec- 
trons in  their  transfer  between  Fe++  and  FC+++. 

Likewise  a  platinum  electrode  immersed  in  a  solution  may  be 
said  to  function  as  an  actual  hydrogen  electrode  only  when  a 
finite  concentration  or  pressure  of  hydrogen  is  known  or  provided. 
For  such  a  pressure  to  be  definite  and  stable  the  solution  must 
be  reduced  to  such  an  extent  that  any  oxidation-reduction  equi- 
librium in  the  solution  is  at  a  state  compatible  with  the  state  of 
the  equilibrium  of  the  reaction: 

2H+  +  2e  ^  H2 

which  is  under  measurement.     This  is  another  way  of  stating 
the  principle  discussed  on  page  244. 

Another  interesting  relation  is  obtained  by  taking  into  consid- 
eration a  certain  hypothetical  relation  between  the  hydrogen 
electrode  and  the  oxygen  electrode.  There  are  reasons  for  be- 
lieving that  an  oxy-hydrogen  gas  cell,  i.e.,  a  cell  composed  of  a 
hydrogen  and  an  oxygen  electrode,  each  under  one  atmosphere 
of  the  respective  gases  should  show  an  E.M.F.  of  1.23  volts  at 
all  pH  values.  It  is  at  once  evident  then  that  an  oxygen  elec- 
trode should  enable  one  to  measure  pH  values  (see  equation  (58)), 
Or  more  directly  pOH  values.  As  a  matter  of  fact  the  oxygen 
electrode"  does  not  work  well  in  practice  and  although  Grube  and 
Dulk  (1918)  believe  that  they  have  obtained  experimental  evi- 
dence for  the  theoretical  relation  between  the  oxygen  electrode 
and  the  hydrogen  electrode,  the  oxygen  electrode  is  by  no  means 
a  practical  instrument.     Why  this  is  so  has  been  a  matter  for 


REDUCTION    POTENTIALS  255 

considerable  debate.  No  satisfactory  explanation  has  been  of- 
fered. If,  however,  we  assume  the  theoretical  relations  as  a  basis 
for  argument,  it  is  evident  from  what  has  already  been  said  that 
we  are  privileged  to  express  the  relations  between  different 
electrodes  in  terms  of  an  oxygen  electrode.  Likewise  it  is  evident 
that  to  obtain  an  actual  oxygen  electrode  potential  it  would  be  neces- 
sary to  oxidize  the  material  in  solution  to  a  point  compatible  with 
a  definite  and  finite  oxygen  pressure. 

Leaving  out  all  question  of  the  numerical  value  of  the  oxy- 
hydrogen  electrode  and  all  question  regarding  the  actuality  of 
a  hydrogen  or  oxygen  pressure  the  genesis  of  equations  (57)  and 
(58)  shows  that  a  system  can  be  defined  in  terms  of  either  a  hy- 
drogen electrode  or  an  oxygen  electrode. 

In  the  second  place  experimental  data  obtained  with  elec- 
trode measurements  alone  do  not  reveal  the  components  which 
enter  into  the  constant  of  an  electrode  potential  equation.  We 
shall  presently  deal  with  some  relations  between  oxidation-reduc- 
tion potentials  and  the  pH  of  the  solution,  and  shall  adopt  for  the 
sake  of  convenience  the  assumption  that  the  reductant  is  an 
anion  created  from  the  oxidant  by  the  introduction  of  one  or  more 
electrons.  But  the  equations  used  to  formulate  the  experimental 
data  require  only  that  proper  relative  relations  be  observed  and 
it  would  be  just  as  legitimate  to  consider  the  relation  between 
oxidant  and  reductant  from  either  of  the  following  points  of 
view: 

OX  +  2e  ^±  RED 

OX  +  H2  ^  hydrogenated  reductant. 

The  same  form  of  electrode  equation  is  obtained  in  either  case 
and  the  decision  between  the  two  points  of  view  is  inextricably 
bound  up  in  the  complex  nature  of  the  constants  which  enter 
into  the  working  equations. 

Thirdly,  it  is  of  great  practical  importance  for  many  studies 
to  note:  that  in  any  case  where  a  definite  potential  difference  is 
to  be  established  at  the  electrode  there  must  be  in  the  system  two 
species,  one  of  which  is  the  direct  or  indirect  reduction  product  of 
the  other,  and  that  the  ratio  of  their  concentrations  or  activities 
must  be  of  finite  magnitude.     Neglect  of  this  principle  is  not 


256  THE    DETERMINATION    OF   HYDROGEN    IONS 

infrequent,  and  is  doubtless  due  to  the  emphasis  which  has  been 
placed  upon  the  final,  working  form  of  the  equation  for  the  dif- 
ference of  potential  betwreen  a  metal  and  a  solution  of  its  ions.  In 
obtaining  the  final  form  of  this  equation  certain  assumptions 
have  been  made  and  the  potential  difference  at  the  electrode  is 
made  to  appear  as  if  it  were  dependent  only  upon  the  concentra- 
tion of  one  species,  namely  the  metal  ions.  Whether  this  be 
the  explanation  or  not,  there  are  not  infrequently  encountered 
in  the  literature  attempts  to  measure  electrode  potential  differ- 
ences with  a  single  oxidant  or  reductant.  It  should  be  plain 
from  a  study  of  figure  39  that,  when  the  oxidant  or  reductant 
alone  is  present,  the  electrode  potential  difference  becomes  asymp- 
totic to  the  Eh  axis.  Were  it  possible  to  eliminate  absolutely 
every  trace  of  the  oxidant,  the  potential  difference  obtained  with 
the  reductant  alone  would  tend  to  become  infinite.  Wherever 
stable  potentials  have  been  reported  as  having  been  found  with 
reductant  alone  it  is  doubtless  due  to  the  presence  of  the  oxidant 
as  an  impurity. 

From  the  foregoing  discussions  it  should  be  evident  that  the 
designation  of  a  particular  electrode-solution  system  depends  so 
far  as  convenience  is  concerned  upon  relations  which  we  seek, 
it  being  more  convenient  in  some  instances  to  formulate  all  data 
in  terms  of  hydrogen  electrode  potentials  and  in  other  instances 
in  terms  of  reduction  potentials.  So  far  as  the  actual  physical 
maintenance  of  electrode  conditions  is  concerned  the  designation 
of  an  electrode  as  of  one  or  the  other  type  will  certainly  depend 
upon  a  finite  ratio  of  two  products,  one  of  which  is  the  reduction 
product  of  the  other;  but  the  discovery  of  what  these  species 
are  is  often  a  most  difficult  problem  for  the  solution  of  which  the 
electrode  equations  by  themselves  are  not  sufficient. 

SOME    ELEMENTARY    RELATIONS    OF    HYDROGEN    ION    CONCENTRA- 
TIONS TO  OBSERVED  "  REDUCTION"  POTENTIALS 

In  dealing  with  an  oxidation-reduction  equilibrium,  as,  for 
instance,  that  between  ferrous  and  ferric  iron,  our  first  concern 
is  with  the  relation  between  electrode  potential  difference  and 
the  ratio  of  the  concentrations  of  the  components  added,  or 
analytically  determined.  Now  it  is  found  that  a  given  ratio  of 
ferric  arid  ferrous  salts  does  not  give  the  same  potential  under 


REDUCTION    POTENTIALS  257 

all  circumstances  as  it  should  if  we  could  substitute  this  fixed 
ratio  in  Peters'  equation.  It  is  convenient  to  assume  that  the 
true  ratio  to  be  substituted  is  the  ratio  of  the  ion  concentrations 
and  when  this  ratio  can  be  found  its  substitution  in  Peters'  equa- 
tion often  yields  a  good  constant.  Alteration  of  the  ion  concen- 
tration from  that  of  the  total  salt  added  may  be  due  to  incomplete 
ionization  of  the  salt  as  added  or  to  the  withdrawal  of  ions  by 
the  formation  of  complexes.  Very  often  the  concentration  of 
the  active  agents  is  determined  by  the  concentration  of  the  hydro- 
gen ions  and  it  is  with  this  that  we  are  now  concerned. 

To  illustrate  the  problem  let  us  assume  that  the  active  oxidant 
is  neither  acidic  nor  basic  so  that  we  can  neglect  any  acidic  or 
basic  dissociation  and  in  dilute  solution  identify  the  active  con- 
centration [OX]  with  the  total  oxidant  [S0].  Let  us  next  assume 
that  on  reduction  an  electron  is  introduced  into  the  body  to 
make  the  reductant  virtually  acidic.  The  concentration  of 
active  reductant  then  becomes  the  concentration  of  the  anion 
of  an  acid.  [RED]  must  be  identified  as  [RED],  and,  when  there 
is  sought  the  relation  between  observed  potentials  and  total 
reductant  and  oxidant,  use  must  be  made  of  the  equation  for 

the  acid  dissociation :     [RED]  =  — — I"   r  *     where  [SJ  is  the  total 

concentration  of  reductant  and  Kais  the  acid  dissociation  con- 
stant for  that  particular  seat  of  ionization  concerned.  Substitut- 
ing the  above  in  equation   (59) 


Eh  =  Ekl-^lnKa+^ 
nF  nF 


lnT^-MH^l-— In^} 
L  J       nF      [S0] 

or  collecting  constants 

Eh=Ek+Hln[K.  +  [H+]]-?flng  (62) 

In  order  to  emphasize  the  effect  of  [H+]  let  us  assume  that  the 

.     [SJ   . 
ratio  — ,  is  to  be  kept  constant  while  [H+]  is  varied.     Inspec- 
ts 

tion  of  (62)  shows  that  while  [H+]  is  large  in  relation  to  Ka,  Eh 

RT 

will  vary  as  -^  In  [H+].     When   [H+]  approaches  and    passes 

Ka,  variation  of  Eh  passes  over  gradually  from  the  relation  indi- 
cated above  to  the  other  extreme  where  there  is  no  appreciable 
variation  of  potential  with  change  in  [H+], 


258  THE   DETERMINATION    OF   HYDROGEN    IONS 

Ordinarily  these  relations  are  not  perceived  because  the  varia- 
tion of  [H+]  is  insufficient,  but  the  principle  involved  is  to  be 
found  in  the  case  of  ferro-ferricyanide  potentials  as  pointed  out 
by  Kolthoff,  and  they  are  more  clearly  to  be  perceived  in  the 
data  on  the  oxidation-reduction  potentials  of  certain  dyes  briefly 
reported  by  Clark  (1920)  and  by  Clark  and  coworkers   (1921). 

Let  us  also  consider  the  equilibria  of  the  quinone-hydroqumone 
system. 

Quinone  +  2d  -ctrons  ;=±  anion  of  hydroquinone 
OCtH40  +  2e^  OC6H40 

If  in  equation  (59)  we  identify  [OX]  as  the  total  concentration 
of  quinone,  [Sq],  then  in  the  same  equation  [RED]  must  be  iden- 
tified as  the  concentration  of  the  divalent  anion  of  hydroquinone 
[TT],    and  n  =  2. 

*-*--wMw  (63) 

If  [Sd]  is  the  total  concentration  of  hydroquinone,  [H2D]  the 
undissociated  hydroquinone,  [HD]  the  first  anion,  [D]  the  second 
anion,  Ki  the  first  acid  dissociation  constant  and  K2  the  second 
acid  dissociation  constant  we  have: 

[hd] [h+]  _   mm  _ ~ 

~vm~  ~    "IhdT  ~    ' 

and 

[Sd]  =  [H2D]  +  [HD]  +  [  D~] 

Solving  the  above  equations  for  [  D  ]  and  substituting  in  (63)  we 
have: 


Eh-Efc-H  lnKaK.+^ln 


[H+l'+KitH+J  +  KxK, 


] 


-—  In  ^3  (64) 

2F      [SJ  K    } 

The  second  term  can  be  combined  with  Ekl  to  give  E'k  as  will 
be  done  later. 

We  shall  consider  only  the  order  of  magnitude  of  Ki  and  K2 
and  their  combined  influence.  Scudder's  tables  give  Ki  = 
1    X  10"10.     Let  K2  be  assumed  to  be  of  the  order  10-11.     Neg- 


REDUCTION   POTENTIALS  259 

lecting  numbers  of  insignificant  orders  of  magnitude  we  find  that 
while  [H+]  is  large  in  relation  to  Ki  and  K2  (higher  than  10~7) 

RT 

the  third  term  in  equation  (64)  reduces  to  +  "^  In  [H+]2. 


Then 


0.000,198T       [Sa]  ,     x 

Eh  =  Ek  -  0.000, 198TpH  -  £ log  — j         (65) 


Thus,  if  the  ratio  of  total  hydroquinone  to  total  quinone  be 
kept  constant,  the  electrode  potential  difference,  Eh,  is  a  linear 
function  of  pH  within  the  limits  of  the  assumptions  made  above. 
A  departure  from  this  relation  should  begin  to  appear  near  pH 
9,  should  become  very  marked  at  pH  10,  and,  if  other  phenomena 
could  be  ruled  out,  Eh  should  no  longer  vary  with  pH  when  pH 
is  larger  than  about  12  provided  the  magnitude  of  K2  has  been 
correctly  guessed. 

The  experimental  data  to  be  mentioned  in  a  later  chapter  indi- 
cate that  the  hydrogen  pressure  in  equilibrium  with  an  equimolec- 
ular  mixture  of  quinone  and  hydroquinone  is  physically  of  an 
entirely  negligible  magnitude. 

As  Biilmann  has  shown  (see  Chapter  XX),  a  platinum  electrode 
in  the  presence  of  a  definite  mixture  of  quinone  and  hydroquinone 
can  be  made  to  measure  pH  values. 

Besides  cases  of  the  type  given  above  we  have  cases  such  as 
that  of  iron  where  the  reaction 

Fe+++  +  e  ^±  Fe++ 

is  essentially  the  destruction  by  the  electron  of  a  point  of  basic 
ionization. 

It  is  also  conceivable  that  the  addition  of  two  electrons  may 
change  an  ampholyte  to  a  diacidic  compound. 

Available  data  are  quite  insufficient  to  show  whether  or  not 
ionizations  at  points  other  than  those  immediately  concerned 
in  the  oxidation-reduction  process  produce  a  marked  effect  upon 
the  point  actually  concerned  in  the  oxidation-reduction  process. 
They  probably  do  for  any  strain  in  the  electronic  forces  at  one  point 
of  a  molecule  must  be  felt  to  some  extent  at  all  other  points. 

There  may  also  be  found  cases  where  the  electronic  fields  of 
force  are  so  altered  by  the  introduction  of  the  electrons  concerned 


260  THE   DETERMINATION    OF   HYDROGEN   IONS 

in  reduction  that  the  reductant,  instead  of  becoming  more  acidic 
or  less  basic  becomes  less  acidic  or  more  basic.  The  system  hemo- 
globin-oxyhemoglobin  comes  to  mind;  but  the  available  data  are 
altogether  too  meagre  to  permit  a  formulation  of  actual  cases, 
or  even  to  permit  an  appraisal  of  the  present  method  of  presenta- 
tion. We  have  only  to  keep  in  mind  the  fact  that,  if  this  method 
of  treatment  proves  to  be  valuable,  there  may  be  found  a  wide 
variety  of  cases  reducible  to  a  form  comparable  with  that  of 
equation  (62).  There  we  find  three  terms.  Of  these  the  middle 
term  is  the  one  which  will  vary  from  case  to  case.  It  will  con- 
tain [H+]  and  the  constants  of  the  oxidation-reduction  equilib- 
rium. This  term  will  determine,  not  only  the  general  form  of  the 
curve  relating  Eh  to  [H+],  but  also  deviation  or  inflexion  points 

fS  1 
when  7£~.  and  n  are  kept  constant  and  [H+]  is  varied. 

Whenever  the  magnitudes  of  the  equilibrium  constants  are  in 

RT 

such  relation  to  [H+]  that  the  middle  term  reduces  to   -^  In 

[H+],  as  it  may  in  (64),  the  electrode  potential  becomes  a  linear 
function  of  pH.  Under  these  limited  circumstances  there  can 
be  calculated  a  hypothetical,  constant,  hydrogen  pressure  by  the 
method  given  at  the  beginning  of  this  chapter, — which  pressure 
may  be  considered  characteristic  for  the  given  equilibrium.  Since 
such  pressures  are  often  of  very  small  magnitude,  and  since  they 
vary  in  magnitude  even  more  than  hydrogen  ion  concentrations, 
it  is  sometimes  convenient  to  use  a  logarithmic  system  of  no- 
tation similar  to  the  pH  of  hydrogen  electrode  work  and  to  let 

log  — —  =  rH,  where  Ph2  is  the  pressure  of  molecular  hydrogen 

in  atmospheres. 

Clark  and  coworkers  have  calculated  rH  values  characteristic 
of  various  oxidation-reduction  indicators.  Examples  are  shown 
in  table  45. 

As  indicated  above  such  rH  values  have  a  limited  significance. 
Even  near  neutrality  the  indigo  system  departs  from  constant 
rH  and  in  a  manner  indicated  by  a  full  equation  comparable  with 
(64). 

The  manner  in  which  the  three  variables — electrode  potential, 
pH  and  percentage  reduction,  are  related  in  certain  cases  is 
illustrated  in  figure  39. 


REDUCTION    POTENTIALS 


261 


When  it  is  desired  to  express  the  state  of  a  solution  without 
regard  to  any  particular  equilibrium  it  is  best  to  return  to  the 
concept  formulated  in  equation  (53)  as  having  the  desired  gener- 
ality. But  lest  terms  such  as  electron  concentration,  pressure 
or  activity  gain  an  unwarranted  appearance  of  reality  through  use, 
and  lest  numerical  values  connected  with  this  concept  be  given 
meanings  too  arbitrary,  it  will  be  best  to  retain  the  use  of  the  elec- 
trode potentials  themselves  and  in  general  to  call  them  reduction 
potentials.  These  specify  with  directness  the  general  state  of  the 
solution. 


TABLE  45 

INDOPHENOL-INDOPHENOL  WHITE 

TETRA  SULFONATES  OF  INDIGO  AND 
OF  INDIGO  WHITE 

pH 

rH 

pH 

rH 

4.36 

21.3 

3.09 

12.2 

5.33 

21.4 

4.51 

12.2 

6.64 

22.0 

5.90      • 

12.3 

7. DO 

21.4 
20.7 

6.48 

12.5 

8.98 

10.23 

20.5 

As  pH  increas 

;s  rH  increases 

Since  a  given  mixture  of  oxidation  and  reduction  products 
at  a  given  pH  stablizes  the  "reduction  potential"  of  a  solution, 
we  have  a  condition  comparable  with  the  buffer  action  in  the 
acid-base  system.  To  distinguish  stabilization  of  oxidation- 
reduction  from  acid-base  buffer  action  we  may  use  the  term 
poising  action.  Thus  a  solution  may  be  said  to  be  poised  at 
a  given  reduction  potential  when  the  addition  or  subtraction 
of  oxidants  or  reductants  does  not  seriously  alter  the  reduction 
potential. 

For  example  in  figure  39,  if  methylene  blue  at  pH  4.6  is  about 
75  per  cent  reduced  we  know  that  the  reduction  potential  of  the 
solution  should  be  at  about  +0.1.  If  quite  appreciable  additions 
of  oxidants  or  reductants  do  not  displace  the  reduction  potential 
very  much  from  this  point  it  is  evident  that  the  solution  is  "  poised" 
at  +  0.1. 

This  brief  outline  will  have  indicated  the  profound  importance 
of  the  hydrogen  ion  concentration  of  a  solution  for  processes  of 


262 


THE  DETERMINATION  OF  HYDROGEN  IONS 


oxidation-reduction.  A  striking  demonstration  is  given  in  a 
lecture  experiment  by  Stieglitz  (1917,  page  292).  Formaldehyde 
in  acid  solution  is  comparatively  inactive  with  silver  ions.  On 
alkalization  of  the  mixture  vigorous  reduction  of  the  silver  occurs. 
It  may  also  be  shown  that  a  proper  mixture  of  ferro-  and  ferri- 
cyanid  is  inactive  toward  indophenol  in  neutral  and  alkaline 
solutions,  that  up  to  acidities  of  pH  4  the  potential  of  the  ferro- 
ferri  mixture  does  not  vary  with  pH  while  that  of  indophenol- 
indophenol  white  does.  At  acidities  near  pH  4  the  two  systems 
run  into  one  another  and  the  indophenol  is  reduced. 


100 


50 


I>vA.tc^O 

*l 

'fl 

•Wry/ 

7 

•ail 

A. 

(i 

I 

JJ 

J 

J 

\             \ 
J 

^f 


+.3 


+A 


-/ 


100' 


S<? 


rr 

r 

;'       ;' 

4 

J 

V 

'         i 

°m.  B\vt 

J 

'J\ 

J 

J 

J 

+,*  +.3         +.2.  +•'  °  -I  -\ 

Fig.  39.  Relation  of  pH  to  Oxidation-Reduction  Equilibria  of  Indigo- 
Indigo  White  and  Methylene  Blue-Methylene  White 

Abscissas:  reduction  potential.  Ordinates:  percentage  reduction.  Fig- 
ures on  curves:  pH  values. 

Finally  it  may  be  said  that  all  oxidation-reduction  equilibria 
do  not  lend  themselves  equally  well  to  potent iometric  study.  An 
enormous  amount  of  experimental  and  theoretical  investigation 
remains  to  be  done. 

In  passing,  it  may  be  mentioned  that  the  instruments  and  many 
of  the  principles  which  have  been  here  described  for  the  determina- 
tion of  hydrogen  ion  concentration  are  applicable  in  the  deter- 


REDUCTION  POTENTIALS  263 

mination  of  oxidation-reduction  equilibria  and  in  the  titration  of 
oxidizing  or  reducing  substances.  The  oxidation-reduction  elec- 
trode with  potentiometric  measurement  has  been  applied  exten- 
sively to  the  determination  of  the  end  points  of  titrations  and  to 
the -study  of  oxidation-reduction  equilibria. 

While  the  effect  of  hydrogen  ion  concentration  has  been  recog- 
nized in  many  of  these  studies  altogether  too  little  use  has  been 
made  of  the  methods  which  have  been  applied  in  biochemistry 
for  the  control  and  measurement  of  pH. 


CHAPTER  XVII 
Sources  of  Error  in  Electrometric^  Measurements  of  pH 

Besides  faults  in  the  potentiometric  system  there  are  a  variety 
of  sources  of  error  which  demand  special  attention.  Some  of 
these  are  specific  to  hydrogen  electrode  work;  others  are  not. 

Sometimes  the  most  trivial  occurrence  may  cause  considerable 
trouble;  such  is  the  bubble  of  gas  that  may  persistently  cling  to 
the  bore  of  a  stopcock  key  which  is  part  of  a  liquid  connection. 
This  is  mentioned  simply  to  emphasize  the  constant  watchfulness 
required  of  the  operator  of  a  hydrogen  electrode  system.  A  well- 
shielded  electrical  system  may  be  put  out  of  commission  in  the 
most  unexpected  way.  Miserly  supply  of  hydrogen  with  which 
to  sweep  out  hydrogen  electrode  vessels  is  perhaps  one  of  the  com- 
monest faults,  but  the  hoarding  of  solutions  which  should  be  used 
to  rinse  away  the  buffer  action  of  solutions  previously  used  in  a 
vessel  may  also  be  serious. 

Aside  from  such  questions  of  technique  there  are  certain  inher- 
ent difficulties  in  the  application  of  the  hydrogen  electrode  method. 

We  have  already  discussed  in  Chapter  XVI  the  relation  between 
the  hydrogen  electrode  and  the  "reduction  electrode,"  and  have 
shown  that  no  true  hydrogen  electrode  potential  can  be  attained 
until  the  solution  is  so  far  reduced  that  it  can  support  one  atmos- 
phere of  hydrogen.  It  is  thus  made  perfectly  obvious  that  a  meas- 
urement of  pH  must  be  preceded  by  a  very  thorough  reduction 
of  the  solution.1 

When  we  speak  of  reduction  we  mean  reduction  in  its  wide  sense 
and  include  among  the  oxidizing  agents  those  metal  ions  which 
at  a  given  concentration  may  be  reduced  by  one  atmosphere  of 
hydrogen. 

The  hydrogen  electrode  if  properly  treated  gives  such  a  pre- 
cisely defined  potential  in  certain  well  buffered  inorganic  solutions, 
reaches  this  potential  so  rapidly,  returns  when  polarized,  and 

1  In  some  instances  it  is  important  to  remember  that  reduction  of  the 
constituents  of  a  solution  may  so  change  the  acidic  or  basic  properties  of 
these  constituents  that  serious  shifts  in  pH  may  occur. 

264 


ERRORS   IN    ELECTROMETRIC   MEASUREMENTS  265 

adjusts  itself  to  temperature  and  pressure  changes  so  well  that  there 
is  little  doubt  of  its  being  a  reversible,  accommodating,  relatively 
quick-acting  electrode.  It  is  perhaps  because  of  this  that  it  shows 
a  hydrogen  electrode  potential  in  solutions  which  could  be  slowly 
reduced  by  hydrogen.  For  instance  certain  culture  media  may 
exhibit  upon  an  electrode  of  platinum  uncharged  with  hydrogen  • 
a  potential  which  is  distinctly  toward  the  oxidizing  region  of  oxi- 
dation-reduction potential.  That  they  are  capable  of  reduction 
and  that  the  first  reduction  potential  is  not  a  pseudo  potential 
is  shown  by  the  orderly  progress  of  the  potential  toward  that  of  a 
hydrogen  electrode  under  the  activity  of  bacteria.  Yet  such 
culture  media  if  treated  in  the  first  place  as  in  making  a  hydro- 
gen electrode  measurement  exhibit  a  fairly  constant  and  repro- 
ducible hydrogen  electrode  potential  the  calculated  pH  value 
from  which  checks  well  with  colorimetric  measurements.  The 
explanation  seems  to  be  that  although  that  complete  reduction 
of  material  to  a  point  where  the  oxidation-reduction  equilibrium 
will  support  an  atmosphere  of  hydrogen  is  not  attained,  there  is 
established  a  virtual  hydrogen  electrode  equilibrium  by  reason 
of  the  rapidity  of  action  between  hydrogen  and  hydrogen  ion  and 
the  slowness  of  action  between  hydrogen  and  oxidizing  agents. 

The  effect  of  an  intense  oxidizing  agent  will  be  at  once  recognized. 
At  the  other  extreme  are  the  cases  where  no  drift  in  the  E.  M.  F. 
in  the  direction  of  an  oxidizing  action  at  the  hydrogen  electrode 
will  be  detected.  Between  these  extremes  lie  the  subtle  uncer- 
tainties which  make  it  advisable  to  check  electrometric  measure- 
ments with  indicator  measurements  and  to  apply  tests  of  repro- 
ducibility, of  the  effect  of  polarization,  of  the  effect  of  time  on 
drift  of  potential  and  all  other  means  available  to  establish  the 
reliability  of  an  electrometric  measurement  in  every  doubtful  case. 

There  are  effects  of  unknown  cause  which  are  included  under 
the  term  "poisoned  electrodes."  An  electrode  may  be  "poisoned" 
by  a  well  defined  cause  such  as  those  to  be  mentioned  presently; 
but  occasionally  an  electrode  will  begin  to  fail  for  reasons  which 
cannot  be  traced.  There  is  hardly  any  way  of  putting  an  ob- 
server on  his  guard  against  this  except  to  call  his  attention  to  the 
fact  that  if  he  is  familiar  with  his  galvanometer  he  will  notice  a 
peculiar  drift  when  balancing  E.  M.  F.'s. 

Arsenic  deposits,  adsorption  of  material  by  the  platinum  black 


266  THE   DETERMINATION    OF   HYDROGEN    IONS 

(with  such  avidity  sometimes  that  redeposition  of  the  black  is 
necessary),  the  deposit  of  films  of  protein,  have  all  been  detected 
as  definite  causes  of  electrode  "poisoning."  Michaelis  (1914) 
places  free  ammonia  and  hydrogen  sulfid  among  the  poisons. 
However,  there  is  no  special  difficulty  in  obtaining  hydrogen 
electrode  potentials  agreeing  with  colorimetric  measurements  in 
bacterial  cultures  containing  distinct  traces  of  ammonia  or  hydro- 
gen sulfid  and  apparently  reliable  measurements  have  been  made 
of  the  pH  values  of  ammonium-ammonium  chloride  mixtures. 
'  Of  the  antiseptics  used  in  biological  solutions  Michaelis  (1914) 
states  that  neither  chloroform  nor  toluol  interfere  if  dissolved. 
He  does  not  mention  that  chloroform  may  hydrolyze  to  hydro- 
chloric acid.  Drops  of  toluol  however  affect  the  electrode. 
Phenol  is  permissible  but  of  course  in  alkaline  solutions  partici- 
pates in  the  acid-base  equilibria. 

There  is  an  extensive  literature  upon  the  so-called  "poisons" 
which  interfere  with  the  catalytic  activity  of  the  finely  divided 
noble  metals  used  on  the  hydrogen  electrode.  This  literature  is 
most  suggestive,  but  there  is  still  need  for  more  direct  studies  of 
the  conditions  surrounding  the  catalytic  activity  of  the  hydrogen 
electrode. 

Simply  for  the  sake  of  clearness  we  may  distinguish  two  func- 
tions of  the  electrode.  The  electrode  is  first  of  all  a  convenient 
third  body  by  which  there  is  established  electrical  connection 
with  the  system  hydrogen-hydrogen  ions.  That  the  equilibrium 
of  this  system  should  not  be  disturbed  by  the  presence  of  a  sub- 
stance "poisoning"  the  catalytic  activity  of  the  platinum  black 
has  been  tacitly  assumed  in  the  derivation  of  the  thermodynamic 
equation  for  electrode  potential  difference.  If  the  reduction  of 
the  solution  could  be  accomplished  without  dependence  upon  the 
catalytic  activity  of  the  electrode  it  should  be  theoretically  possi- 
ble to  attain  a  true  hydrogen  electrode  potential  even  in  the  pres- 
ence of  a  "poison."  However,  in  ordinary  practice  an  electrode 
is  used  not  only  as  an  electrode  per  se  but  also  as  a  hydrogenation 
catalyst.  As  such  it  is  very  sensitive  to  "poisons."  "Poisons" 
are  then  to  be  regarded  as  the  cause  of  sluggish  electrodes.  Among 
these  we  find  all  degrees.  Hydrogenation  to  a  point  compatible 
with  a  true  hydrogen  electrode  potential  may  be  delayed  but 
slightly  and  we  may  say  that  the  electrode  is  a  bit  slow  in  attain- 
ing a  stable  potential  without  our  ever  suspecting  a  "poison;" 


«  ERRORS   IN    ELECTROMETRIC   MEASUREMENTS  267 

or  the  black  metal  may  be  so  seriously  injured  that  it  becomes 
entirely  impractical  to  await  equilibrium. 

And  just  as  "  poisons"  may  render  an  electrode  useless  for  practi- 
cal measurements,  so  the  employment  of  accelerators  of  catalysis 
may  promote  efficiency.  With  the  exception  of  a  brief,  unpublished 
note  by  Bovie  little  work  has  been  done  in  this  direction. 

From  what  has  already  been  said  the  effect  of  the  presence  of 
oxygen  is  obvious.  Indifferent  gases  such  as  nitrogen  may  be 
considered  merely  as  diluents  of  the  hydrogen  and  as  such  must 
be  taken  into  consideration  in  accurate  estimations  of  the  partial 
pressure  of  hydrogen.  Gases  like  carbon  dioxid  on  the  other 
hand  act  not  only  as  diluents  but  also  become  components  of 
any  acid-base  equilibrium  established  in  their  presence. 

In  very  many  instances  biological  fluids  contain  carbonate  and 
the  double  effect  of  the  carbon  dioxid  upon  the  partial  pressure 
of  the  hydrogen  and  upon  the  hydrogen  ion  equilibria  render  accu- 
rate measurements  difficult  unless  both  effects  are  taken  into  con- 
sideration and  put  under  control. 

At  high  acidities  in  the  neighborhood  of  pH  5  carbon  dioxide 
will  have  relatively  little  effect  upon  a  solution  buffered  by  other 
than  carbonates.  As  the  pH  of  solutions  increases  the  participa- 
tion of  C02  in  the  acid-base  equilibria  becomes  of  more  and  more 
importance.  The  C02  partial  pressure  in  equilibrium  with  the 
carbonates  of  a  solution  is  a  function  of  both  the  pH  and  the 
total  carbonate.  If,  however,  we  consider  for  the  sake  of  the 
argument  that  the  total  carbonate  remains  fairly  low  and  constant, 
the  C02  partial  pressure  becomes  less  with  increase  in  pH  while 
its  effect  upon  the  hydrogen  ion  equilibria  increases  with  increase 
in  pH.  Therefore  it  may  be  said  that  it  is  of  more  importance 
under  ordinary  conditions  to  maintain  the  original  C02  content 
of  the  solution  than  it  is  to  be  concerned  about  the  effect  of  C02 
upon  the  partial  pressure  of  the  hydrogen.  Furthermore  the 
effect  of  diminishing  the  partial  pressure  of  the  hydrogen  is  of 
relatively  small  importance. 

For  these  reasons  the  bubbling  of  hydrogen  through  the  solu- 
tion is  to  be  avoided  unless  one  cares  to  determine  the  partial 
pressure  of  C02  which  must  be  introduced  into  the  hydrogen  to 
maintain  the  carbonate  equilibria  and  then  provides  the  proper 
mixture  (Hober).  The  method  usually  employed  is  to  use  a  vessel 
such  as  that  of  Hasselbalch,  of  McClendon  or  of  Clark  in  which  a 


268  THE    DETERMINATION    OF   HYDROGEN    IONS  ♦ 

preliminary  sample  of  the  solution  can  be  shaken  to  provide  the 
solution's  own  partial  pressure  of  C02,  and  in  which  there  is  provi- 
sion for  the  introduction  of  a  fresh  sample  with  its  full  C02  pressure. 
The  hydrogen  supply  is  then  kept  at  atmospheric  pressure  and 
the  partial  pressure  of  hydrogen  in  the  electrode  vessel  is  either 
considered  to  be  unaffected  by  the  C02  pressure  or  corrected  from 
the  known  C02  pressure  of  the  solution  under  examination. 

Of  course  in  cases  where  the  total  carbonate  in  solution  rises  to 
considerable  concentrations  the  partial  C02  pressure  may  become 
of  very  significant  magnitude  and  its  effect  in  lowering  the  hydro- 
gen pressure  must  be  carefully  considered. 

In  determining  the  hydrogen  ion  concentration  of  the  blood  by 
the  electrometric  method  the  two  outstanding  difficulties  encoun- 
tered are  the  presence  of  carbonate  and  oxyhemoglobin.  If  hy- 
drogen is  swept  through  the  fluid  it  will  remove  so  much  of  the 
C02  that  the  hydrogen  ion  concentration  is  lowered.  If  hydrogen 
is  not  swept  through,  the  C02  will  escape  into  the  hydrogen  at- 
mosphere about  the  electrode  and  reduce  the  partial  pressure  of 
the  hydrogen.  The  oxygen  present  in  the  oxyhemoglobin  "de- 
polarizes" the  hydrogen'  electrode  and  makes  necessary  the 
employment  of  the  plasma. 

Evans  (1921)  has  maintained  that  in  the  electrometric  measure- 
ment of  carbonate  solutions  the  carbonate  is  reduced  to  formate 
and  that  for  this  reason  previous  measurements  of  the  pH  of 
blood  have  been  in  error.  There  are  various  theoretical  reasons 
for  doubting  the  validity  of  Evans'  last  conclusion;  but  since  the 
question  is  one  of  fact  Cullen  and  Hastings  (1922)  have  investi- 
gated the  matter  and  have  failed  to  confirm  Evans. 

The  criterions  of  a  good  hydrogen  electrode  measurement  are 
difficult  to  place  upon  a  rigid  basis  but  certain  practical  tests 
are  easy  to  apply.  Reproducibility  of  an  E.  M.  F.  with  different 
electrodes  and  different  vessels  is  the  foremost  test  of  reliability, 
but  not  a  final  test.  Second  is  the  stability  of  this  E.  M.  F.  when 
attained.  It  is  not  always  practicable  to  distinguish  between  a 
drift  due  to  alteration  in  the  difference  of  potential  at  liquid 
junctions  and  a  drift  at  the  electrode  but  in  most  cases  the  drift 
at  the  liquid  junction  is  less  rapid  and  less  extensive  than  a  drift 
at  the  electrode  when  the  latter  is  due  to  a  failure  to  establish  a 
true  hydrogen-hydrogen  ion  equilibrium.  A  test  which  is  some- 
times applied  is  to  polarize  the  hydrogen  electrode  slightly  and 


ERRORS   IN    ELECTROMETRIC   MEASUREMENTS  269 

then  see  if  the  original  E.  M.  F.  is  reestablished.  This  may. be 
done  sufficiently  well  by  displacing  the  E.  M.  F.  balance  in  the 
potentiometer  system.  Where  salt  and  protein  errors  do  not  in- 
terfere the  gross  reliability  of  a  hydrogen  electrode  measurement 
may  be  tested  colorimetrically.  This  checking  of  one  system  with 
the  other  is  of  inestimable  value  in  some  instances  as  it  has  proved 
to  be  in  the  study  of  soil  extracts.  There  the  possibilities  of  vari- 
ous factors  interfering  with  any  accurate  measurement  of  hydrogen 
ion  concentration  dimmed  the  courage  of  investigators  until  Gil- 
lespie (1916)  demonstrated  substantial  agreement  between  the 
two  methods.  Subsequent  correlation  of  various  phenomena 
with  soil  acidity  so  determined  has  now  established  the  useful- 
ness of  the  methods. 

In  addition  to  the  tests  so  far  mentioned  there  remains  the  test 
of  orderly  series.  Certain  of  the  general  relations  of  electrolytes 
are  so  well  established  that,  if  a  solution  be  titrated  with  acid  or 
alkali  and  the  resulting  pH  values  measured,  it  will  be  known  from 
the  position  and  the  shape  of  the  "titration  curve"  whether  the 
pH  measurements  are  reasonable  or  not.  This  of  course  is  a 
poor  satisfaction  if  there  is  any  reason  to  doubt  the  measurements 
in  the  first  place  but  it  is  a  procedure  not  be  scorned. 

In  dealing  with  protein  solutions  Robertson  (1910)  found  that 
the  electrode  was  injured  by  deposits  of  protein  which  he  as- 
cribed to  acid  coagulation  of  the  protein  by  the  acid  absorbed 
in  the  platinum  black  from  previous  measurements.  Robertson 
therefore  recommends  that  in  a  series  of  measurements  with 
protein  solutions  the  series  be  treated  from  the  alkaline  to  the 
acid  solutions.  If  his  explanation  be  true  there  are  instances 
where  the  reverse  procedure  should  be  followed.  See  sections 
on  isoelectric  points. 

Not  infrequently  the  attempt  is  made  to  measure  electrometri- 
cally  the  pH  value  of  an  unbuffered  solution  such  as  that  of  KC1. 
It  is  not  entirely  the  fault  of  the  method  but  rather  of  the  nature 
of  the  solution  that  this  is  a  task  requiring  the  very  highest 
refinements  known  to  experimental  art.  If  for  the  sake  of  the 
argument  we  assume  that  the  solution  under  examination  is  that 
of  a  perfectly  neutral  salt  having  under  ideal  conditions  a  hydro- 
gen ion  concentration  of  0.000,000,1  N,  a  simple  calculation  will 
show  what  an  enormous  displacement  in  pH  will  be  caused  by 
the  admittance  of  the  slightest  trace  of  CO2  from  the  atmosphere, 


270  THE   DETERMINATION   OF   HYDROGEN    IONS 

of  alkali  from  a  glass  container,  of  impurities  occluded  in  the 
electrode  or  of  impurities  carried  into  the  solution  with  the  sol- 
vent or  solute.  Conversely,  even  if  the  measurement  were  such 
as  to  give  the  true  value  under  ideal  conditions  it  would  have 
little  practical  significance  because  of  the  difficulty  in  holding  the 
conditions  ideal. 

By  the  same  reasoning  it  appears  probable  that  it  would  be 
difficult  to  obtain  true  electrode  potentials  even  with  a  potentio- 
metric  system  drawing  no  current  during  its  adjustment.  When 
no  buffer  is  present  there  is  a  negligible  reserve  of  hydrogen  ions. 
But  the  introduction  of  the  electrode  with  its  enormous  surface 
must  displace  the  equilibrium.  How  much  the  displacement 
will  be  depends  both  on  relative  proportions  of  electrode  and 
solution  and  on  the  technique  used. 

The  effect  of  temperature  variations  upon  the  accuracy  of 
electrometric  measurements  is  a  question  upon  which  it  is  difficult 
to  pass  judgment.  Of  course,  if  measurements  are  not  intended 
to  be  refined  one  may  assume  the  temperature  of  the  room  to  be 
the  temperature  of  the  system  at  the  moment  of  the  electrical 
measurement.  It  is  then  a  simple  matter  to  select  from  tables 
the  values  and  factors  applicable  at  the  selected  temperature. 
Since  such  a  procedure  introduces  errors  which  are  not  serious 
for  many  purposes  the  author's  insistence  upon  temperature  regu- 
lation has  been  criticized.  Those  who  take  this  position  are  doubt- 
less able  to  escape  the  psychological  effects  of  uncertainty,  but 
they  can  hardly  escape  the  inconvenience  of  having  to  deal  with 
new  values  and  new  factors  with  every  shift  in  temperature. 
Temperature  control  so  simplifies  rough  measurements  that  much 
.time  is  saved,  and  for  this  reason  is  recommended  even  when  it 
is  unnecessary.  But  before  the  practice  of  neglecting  tempera- 
ture control  can  have  scientific  standing  it  needs  more  experi- 
mental investigation  than  it  has  been  accorded.  Calculations 
are  quite  insufficient  -for  we  have  little  data  upon  the  hysteresis 
in  the  adaptation  of  different  systems  to  temperature  variation. 

Cullen  (1922),  finding  that  the  temperature  in  an  electrode 
vessel  is  seldom  that  of  the  surrounding  air  in  a  room  subject  to 
temperature  variation,  has  devised  a  modification  of  the  Clark 
electrode  vessel  whereby  the  temperature  of  the  solution  can  be 
measured.  The  same  modification  can  easily  be  made  in  a  calo- 
mel electrode  vessel. 


•     CHAPTER  XVIII 

Standard    Solutions    for   Checking   Hydrogen    Electrode 

Measurements 

Id.  the  routine  measurement  of  hydrogen  ion  concentrations  it 
is  desirable  to  frequently  check  the  system.  To  do  so  in  detail 
is  a  matter  of  considerable  trouble ;  but  if  a  measurement  be  taken 
upon  some  solution  of  well  defined  pH,  and  it  is  found  that  the 
potential  of  the  chain  agrees  with  that  determined  by  careful  and 
detailed  measurements  upon  all  parts,  it  is  reasonably  certain 
that  the  several  sources  of  E.  M.  F.  are  correct. 

Any  one  of  the  buffer  mixtures  whose  pH  value  has  been  estab- 
lished may  be  used  for  this  purpose,  but  there  are  sometimes 
good  reasons  for  making  a  particular  choice. 

S0rensen  (1909)  used  a  mixture  of  8  volumes  of  standard  gly- 
cocoll  solution  to  2  volumes  of  standard  hydrochloric  acid  solution 
for  the  details  in  the  preparation  of  which  see  page  109.  Michaelis 
(1914)  recommends  what  has  come  to  be  known  as  "standard  ace- 
tate." This  is  a  solution  tenth  molecular  with  respect  to  both 
sodium  acetate  and  acetic  acid.  Its  preparation  and  hydrogen 
electrode  potential  at  18°C.  have  been  carefully  studied  by  Wal- 
pole  (1914).     Walpole  proposes  two  methods  for  its  preparation: 

(1)  From  N-sodium  hydroxid  solution  free  from  carbon  dioxid  and 
N-acetic  acid  adjusted  by  suitable  titration  (using  phenolphthalein),  so  as 
to  be  exactly  equivalent  to  it. 

(2)  From  N-sodium  acetate  and  N-acetic  acid  adjusted  by  titration  of 
a  baryta  solution,  the  strength  of  which  is  known  exactly  in  terms  of  the 
N-hydrochloric  acid  solution  used  to  standardize  electrometrically  the 
normal  solution  of  sodium  acetate  . 

Walpole  defines  N-sodium  acetate  as  a  "solution  of  pure  sodium 
acetate  of  such  concentration  that  when  20  cc.  are  taken,  mixed 
with  20  cc.  of  N-hydrochloric  acid,  and  diluted  to  100  cc.  the 
potential  of  a  hydrogen  electrode  in  equilibrium  with  it  is  the  same 
as  that  of  a  hydrogen  electrode  in  equilibrium  with  a  solution  0.2 
normal  with  respect  to  both  acetic  acid  and  sodium  chloride." 
By  mixing  the  N-acetate  with  the  N-HC1  in  accordance  with  this 

271 


272 


THE  DETERMINATION  OF  HYDROGEN  IONS 


definition  and  then  determining  the  potential  of  a  hydrogen  elec- 
trode in  equilibrium  with  it  Walpole  shows  that  the  N-sodium 
acetate  solution  may  be  accurately  standardized.  In  the  fol- 
lowing table  are  given  Walpole's  values  showing  the  relation  of 


TABLE  46 


CUBIC  CENTIMETERS  OF  N/1  HC1  TO  20  CUBIC 

CENTIMETERS  N/1   NaAc  DILUTED 

TO  100  CUBIC  CENTIMETERS 

E.  M.  F. 

19.00 

0.5270 

19.40 

0.5155 

19.50 

0.5125 

19.90 

0.4945 

20.00 

0.4898 

20.39 

0.4712 

20.89 

0  4549 

21.00 

0.4525 

the  E.  M.  F.  of  the  chain:  Hg  |  Hg2Cl2  KC1  (0.1m)  |  KC1  (sat.)  |  Ace- 
tate |  H2Pt  at  18°,  to  the  cubic  centimeters  of  N-HCladdedto20cc. 
N-sodium  acetate  and  diluted  to  100  cc.     If,  for  instance,  the 

potential  found  is  0.4800  volts,  the  ratio  

Concentration  of  Na  Ac 

Hence  the  sodium  acetate  is  0.9901N. 


is 


20.2 
20.0' 


These  values  are  more  convenient  to  use  if  plotted  as  Walpole 
has  done. 


TABLE  47 


TEMPERATURE 

E.  M.  F. 

TEMPERATURE 

E.  M.  F. 

15 

0.5170 

21 

0.5180 

16 

0.5171 

22 

0.5183 

17 

0.5172 

23 

0.5186 

18 

0.5174 

24 

0.5190 

19 

0.5175 

25 

0.5195 

20 

0.5178 

34-38 

0.5200-0.5205 

Walpole  found  that  the  E.  M.  F.  of  the  chain:  Pt  H2 1  "standard 
acetate"  |sat.  KC1|  0.1m  KC1  Hg2Cl2|  Hg  at  18°C.  is  0.6046.  The 
contact  potential  still  to  be  eliminated  was  estimated  by  the 
Bjerrum  extrapolation  to  be  0.0001  volt.     Hence  the  true  poten- 


STANDARDS    FOR   CHECKING 


273 


tial  is  0.6045.  This  value  seems  to  be  the  value  of  the  chain 
corrected  to  one  atmosphere  hydrogen  plus  vapor  pressure. 

Michaelis  (1914)  gives  the  values  in  table  47  for  the  difference  of 
potential  between  the  saturated  KC1  calomel  electrode  and  the 
hydrogen  electrode  in  his  standard  acetate. 

It  will  be  noted  that  both  S0rensen's  standard  glycocoll  and  the 
standard  acetate  solutions  must  be  constructed  by  adjustment  of 
the  components.  While  there  is  no  great  difficulty  in  this  there 
remain  the  labor  and  the  chance  of  error  that  are  involved.     Clark 


PH 


\ 

KHFhtkiUtc 

C.C. 


10 


Fig.  40.  Titration  of  Phthalic  Acid  with  KOH 


and  Lubs  (1916)  have  shown  that  acid  potassium  phthalate  pos- 
sesses, a  unique  combination  of  qualities  desirable  for  the  standard 
under  discussion.  The  first  and  second  dissociation  constants  of 
phthalic  acid  are  so  close  to  one  another  that  the  second  hydro- 
gen comes  into  play  before  the  first  is  completely  neutralized  (see 
fig.  40).  As  a  consequence  the  half-neutralized  phthalic  acid 
(KHPhthalate)  exhibits  a  good  buffer  action.  The  salt  of  this 
composition  crystallizes  beautifully  without  water  of  crystalliza- 


274 


THE   DETERMINATION   OF   HYDROGEN   IONS 


* 


Pi 


tion,  and,  as  was  shown  .by  Dodge  (1915)  and  confirmed  by 
Hendrixson  (1915)  it  is  an  excellent  substance  for  the  standard- 
ization of  alkali  solutions.  As  such  it  is  used  to  standardize  the 
alkali  entering  into  the  buffer  mixtures  of  Clark  and  Lubs  (see 
page  102) .  The  outstanding  feature  is  that  the  ratio  of  acid  to 
base  is  fixed  by  the  composition  of  the  crystals  and  not  by  ad- 
justment as  in  other  standards.  The  salt  may  be  dried  at  105°C. 
and  accurate  concentrations  constructed.  The  diffusion  potential 
against  saturated  KC1  is  somewhat  higher  than  that  of  standard 
acetate  as  estimated  by  the  Bjerrum  extrapolation  but  not  so 
high  as  to  make  good  readings  difficult. 
Clark  and  Lubs  (1916)  found  for  the  chain: 

.      HgHg2Cl2  |  KC1  (saturated)  |  M/20  KHPhthalate  |  H2  Pt 

at  20°C.  an  E.  M.  F.  of  0.4807  corrected  to  one  atmosphere  of 
.  hydrogen.     Their  saturated  calomel  electrode  was  0.0882  volt 
more  negative  than  the  average  of  a  set  of  tenth  normal  calomel 
I  electrodes.     Assuming  0.3379  (cf.  Chapter  XIX)  as  the  value  of 
•  the  tenth  normal  calomel  electrode  and  0.0004  volt  for  the  dif- 
fusion potential  still  to  be  eliminated,  the  hydrogen  electrode 
potential  of  M/20  KHPhthalate  at  20°  is  0.2306. 

LJnfortunately  the  temperature  relations  of  such  chains  are  not 
accurately  known.  For  ordinary  work  the  pH  of  M/20  KHPhtha- 
late may  be  considered  as  3.97  between  20°  and  30°C.  Assuming 
a  liquid  junction  potential  difference  of  0.0004  volts  we  can  reckon 
from  these  data  the  following  total  electromotive  forces  at  various 
temperatures  of  the  chain : 


Calomel  electrode  of  KC1  cone.  X 


Sat.  KC1 


Hydrogen  electrode 
at  one  atmosphere 
in      KHPhthalate 


(i) 


STANDARDS    FOR   CHECKING 


275 


TABLE  48 


TOTAL  E.  M.  F. 

X  =  0.lM 

X=1.0m 

X=saturated  KC1 
(approximate) 

18 
20 
22 
24 
26 
28 
30 

0.5675 
0.5689 
0.5704 
0.5719 
0.5733 
0.5748 
0.5763 

0.5158 
0.5170 
0.5181 
0.5192 
0.5204 
0.5215 
0.5227 

0.4800 
0.4802 
0.4806 
.     0.4812 
0.4817 
0.4822 
0.4827 

These  values  are  entirely  provisional  ftfr  temperatures  other 
than  20°C.  and  require  experimental  verification  before  they  can 
be  used  for  precise  standards.  They  are  given  as  convenient 
standards  for  ordinary  check  measurements. 


CHAPTER  XIX 
Standardization  of  pH  Measurements 

In  the  development  of  the  theory  of  electrolytic  dissociation 
the  hydrogen  electrode  came  upon  the  scene  comparatively  late 
and  after  many  of  the  quantitative  relations  had  been  established 
by  conductance  data.  It  was  therefore  natural  that  these  data 
should  have  been  accepted  in  the  standardization  of  potentio- 
metric  measurements.  It  now  appears  that  the  interpretation  of 
conductance  data  is  more  complicated  than  at  first  supposed  and 
that  certain  of  the  values  that  have  been  used  in  the  standardiza- 
tion of  potentiometric  measurements  are  in  doubt.  The  resulting 
confusion  demands  careful  consideration. 

Let  us  review  briefly  the  way  in  which  conductance  data  enter 
into  the  potentiometric  system. 

The  following  equation  relates  the  potential  difference,  E,  at 
a  hydrogen  electrode  to  the  partial  pressure,  P,  of  hydrogen,  the 
concentration  of  hydrogen  ions,  C,  and  the  constant  K, 

RT     VP 
F        c 

As  shown  in  a  previous  chapter  we  are  forced  to  one  or  an- 
other set  of  comparisons  such  as  is  found  in  a  concentration  cell 
where  P  and  K  are  constant.  In  this  case  we  have  a  measurable 
electromotive  force  and  the  relation 

RT     d 
E.  M.  F.  =  ^rlnTT 

Thus  we  determine  the  ratio  of  two  hydrogen  ion  concentra- 
tions if  the  solutions  are  sufficiently  dilute  to  permit  the  applica- 
tion of  the  gas  laws  from  which  the  above  equation  was  derived. 
To  apply  this  equation  directly  to  the  determination  of  either 
concentration  Ci  or  C2  the  other  concentration  must  be  known. 
Conductance  data  have  been  relied  upon  to  furnish  the  known 
concentration. 

Likewise,  when  a  chain  composed  of  a  calomel  electrode  and  a 

276 


STANDARDIZATION    OF   pH    MEASUREMENTS  277 

hydrogen  electrode  is  used,  the  value  assigned  to  the  calomel  elec- 
trode is  such  that  when  it  is  subtracted  from  the  total  E.  M.  F. 
of  tr?e  chain  the  resulting  E.  M.  F.  is  as  if  between  a  normal  hy- 
drogen electrode  and  the  hydrogen  electrode  under  measurement. 
This  implies  the  experimental  determination  of  the  difference  of 
potential  between  a  normal  hydrogen  electrode  and  the  calomel 
electrode  or  else  between  the  calomel  electrode  and  a  hydrogen 
electrode  in  some  solution  of  known  hydrogen  ion  concentration. 
To  determine  this  known  hydrogen  i«n  concentration  conductance, 
data  upon  hydrochloric  acid  solutions  have  been  relied  upon. 

Unfortunately  hydrochloric  acid  solutions  exhibit  the  so-called 
anomalies  of  strong  electrolytes  which  have  already  been  mentioned. 
Although  it  was  known  from  the  first  that  hydrochloric  acid  solu- 
tions do  not  obey  the  dilution  law ,  it  was  supposed  that  the  ratio 
of  the  equivalent  conductances  at  dilution  v  and  at  infinite  dilution 
(where  there  is  complete  dissociation)  would  give  the  percentage 
ionization  at  dilution  v  and  hence  the  hydrogen  ion  concentration 
at  this  dilution.  However,  this  conclusion  involves  the  assump- 
tion that  the  mobilities  of  the  ions  remain  unaltered  between 
dilution  v  and  infinite  dilution.  Jahn  (1900)  and  Lewis  (1912) 
have  questioned  this  assumption  and  within  recent  years  the  con- 
clusion has  become  firmly  established  among  many  investigators 
that  the  mobilities  do  change  or  else  that  the  chemical  activity  of 
the  ions  of  strong  electrolytes  is  not  strictly  proportional  to  their 
concentration.  In  other  words  conductance  data  alone  are  not 
sufficient  to  define  with  precision  the  hydrogen  ion  concentrations 
of  the  hydrochloric  acid  solutions  which  have  been  used  to  stand- 
ardize the  hydrogen  electrode  system  of  concentration  chains. 
In  support  of  this  contention  there  have  been  brought  forward 
comparisons  of  the  concentration  chains  themselves.     There  is 

Ci 

evidence  that  the  ratio  —  in  the  concentration  chain  formula 

is  not  necessarily  determined  with  accuracy  when  a  measurement 
of  the  E.  M.  F.  of  such  a  chain  is  taken.  What  is  it  then  that  is 
determined?  The'  way  in  which  this  question  will  be  answered 
will  doubtless  form  another  interesting  chapter  in  the  philosophy 
of  science.  Focused  upon  this  point  are  two  tendencies;  the  one 
seeking  to  find  the  factors  which  interfere  with  the  application  of 
the  simple  gas  laws  so  that  the  experimental  data  may  be  corrected 


278  THE   DETERMINATION   OF   HYDROGEN    IONS 

to  apply  to  the  "ideal;"  the  other  seeking  to  formulate  either  the 
empirical  data  or  the  thermodynamic  relations  without  special 
reference  to  the  mechanisms  involved.  • 

It  was  an  astute  suggestion  of  Lewis  (1907)  that  the  simple 
thermodynamic  relations  be  assumed  to  hold,  not  for  concentra- 
tion pressure  relations,  but  for  quantities  which,  when  introduced 
into  the  equations  embodjdng  the  gas  laws,  will  make  these  laws 
apply.  The  two  new  quantities  are  activity  and  fugacity.  In  the 
special  case  of  a  "perfect"  solution,  a  very  dilute  solution,  obeying 
the  laws  of  gases,  activity  and  fugacity  are  equal  to  concentration 
and  pressure  respectively.  But  when  a  solute  ceases  to  conduct 
itself  in  accord  with  the  laws  of  gases,  its  fugacity  and  activity 
remain  such  that  the  equations  which  apply  to  "perfect"  solutions 
still  hold. 

Stated  in  the  above  manner  it  may  appear  to  those  who  insist 
upon  looking  for  the  means  of  applying  concentration  relations  as 
if  Lewis  had  made  use  of  a  clever  dodge.  In  reality  he  has  simply 
expressed  in  a  form  which  he  has  developed  into  a  self-consistent 
system  that  which  is  the  more  directly  determined  experimentally. 
This  is  at  once  evident  in  the  definition  of  activity  by  the  fol- 
lowing postulates. 

1.  When  the  activity  of  a  substance  is  the  same  in  two  phases,  that 
substance  will  not  of  itself  pass  from  one  phase  to  the  other.  2.  When 
the  activity  of  a  substance  is  greater  in  one  phase  than  in  another,  the  sub- 
stance will  pass  from  the  one  phase  into  the  other,  when  they  are  brought 
together. 

With  these  postulates  Lewis  proceeds  to  develop  a  self-consist- 
ent system  in  which  it  appears  that  in  a  "concentration  cell"  the 
ratio  of  activities  is  related  to  the  E.  M.  F.  by  the  equation 

_  ,,  _        RT  ,     activity  1 

E.  M.  F.  =  —  In  ^— 

nF       activity  2 

Only  at  infinite,  or  very  high  dilution,  when  a  solution  approaches 
an  "ideal"  solution,  does  the  more  familiar  relation  of  concentra- 
tion hold  true.  So  long  as  the  limitations  were  well  understood  it 
was  permissible  to  speak  of  the  hydrogen  electrode  method  -as  a 
means  of  determining  relative  concentrations.  If  one  is  willing  to 
use  Lewis'  terms  he  would  be  more  precise  to  speak  of  the  hydro- 


STANDARDIZATION    OF   pH    MEASUREMENTS  279 

gen  electrode  method  as  a  means  of  determining  relative  hydrogen 
ion  activities. 

We  may  note  at  this  point  that  if  we  adopt  the  activity  con- 
cept and  if  we  refer  electrode  potential  differences  to  that  of  the 
normal  hydrogen  electrode,  confusion  is  introduced  by  the  use 
of  the  term  normal  concentration  in  the  definition  of  the  normal 
hydrogen  electrode.  This  is  clarified  if  we  adopt  the  definition 
of  Lewis  and  .Randall:  "A  solution  is  said  to  be  at  (hypothet- 
ical) molar  concentration  with  respect  to  hydrogen  ion  when  the 
activity  of  hydrogen  ion  in  this  solution  is  n  times  as  great  as  in 
1/n  M  solution  of  hydrogen  ion,  where  n  is  a  large  number."  | 

The  use  of  the  equation  given  above  instead  of  the  equation 
involving  concentrations  only  shifts  our  immediate '  problem  to 
a  new  position.  We  are  still  concerned  with  a  ratio  and  must 
somehow  establish  a  point  of  reference.  At  first  sight  we  have 
also  shifted  to  a  position  from  which  it  is  difficult  to  obtain  any 
connection  with  weights  of  materials  (concentrations). 

A  formal  relation  between  activity  and  concentration  may  be  set  up 
by  the  use  of  the  socalled  activity  coefficient.  Of  this  Lewis  and  Randall 
(1921)  state:  '  The  term  activity  coefficient  has  been  used  in  two  senses, 
sometimes  to  mean  the  ion  activity  divided  by  the  assumed  ion  molality, 
and  sometimes  to  express  the  ion  activity  divided  by  the  gross  molality 
of  the  electrolyte." 

Now,  if  we  have  a  solution  of  HC1  so  dilute  that  we  may  assume 
the  activity  of  the  hydrogen  ion  equal  to  the  concentration, 
and  if  at  the  same  time  the  solution  is  so  dilute  that  we  may  assume 
complete  ionization,  we  have  a  starting  point,  for  then  the  hydro- 
gen ion  activity  may  be  determined  from  the  analytical  concen- 
tration of  the  HC1.  By  the  use  of  the  electromotive  force  equation 
relating  activities  we  can  establish  by  experiment  the  relative 
activity  of  the  hydrogen  ion  in  a  more  concentrated  solution. 
But  there  is  little  assurance  that  such  measurements  of  relative 
ictivity  have  been  made  with  the  highest  accuracy  because  of 
he  experimental  and  theoretical  difficulties  of  liquid  junction 
Dotential  differences. 

By  means  of  conductivity  some  idea  is  obtained  of  ion  concentrations 
nd  by   means   of   activity   coefficients   activity   and    concentration    are 


280  THE    DETERMINATION   OF   HYDROGEN    IONS 

related.     But  since  exact  treatment  of  the  subject  necessitates  discussion 
of  assumptions  the  reader  is  referred  to  the  original  literature. 

Using  the  most  probable  values  for  the  corrected  degree  of 
dissociation  of  hydrochloric  acid  solutions,  the  E.  M.  F.  of  the 
cell:  normal  calomel  electrode-hydrogen  electrode  in  N/10  or 
N/100  HC1,  and  the  estimated  contact  potential  difference  at  the 
liquid  juncture,  Lewis  and  Randall  obtained  the  value  0.2776  for 
the  difference  of  potential  between  the  normal  calomel  and  the 
normal  hydrogen  electrodes  at  25°.  This  value  was  revised  to 
0.2828  by  Lewis,  Brighton  and  Sebastian  (1917).  Direct  compari- 
son with  N/10  KC1  calomel  electrode,  as  will  be  noted  later,  gave 
0.3357  as  the  potential  value  of  this  electrode  including  a  slight 
liquid  junction  potential  difference. 

Now  let  us  consider  the  values  hitherto  used  in  biochemical 
work. 

In  S0rensen's  work,  published  prior  to  the  adoption  of  the  pres- 
ent standard  value  of  the  Weston  standard  cell,  the  basis  for  the 
particular  cell  whose  value  he  gave  was  not  stated.  If  it  was  the 
1.01863  used  in  Germany  prior  to  1911  the  correction  of  S0ren- 
sen's  data  to  the  present  international  volt  will  not  be  significant. 
Doubtless  the  international  standard  was  used  in  Denmark  when 
S0rensen  (1912)  published  the  summary  of  the  data  of  S0rensen 
and  Koefoed.  Their  values  involve  two  assumptions;  first  that 
liquid  junction  potential  differences  were  eliminated  by  the  Bjer- 
rum  extrapolation;  second,  that  in  the  calculation  of  the  theoreti- 
cal difference  of  potential  between  the  normal  hydrogen  electrode 
and  the  hydrogen  electrode  in  the  hydrochloric  acid  solutions 
used,  the  correct  hydrogen  ion  concentration  was  given  by  con- 
ductance data.  As  already  stated  there  is  serious  doubt  of  the 
validity  of  the  last  assumption.  Even  so  we  ought,  by  using  the 
same  degree  of  dissociation  for  hydrochloric  acid  solutions,  to 
reconcile  S0rensen's  value  with  that  of  Lewis,  Brighton  and  Se- 
bastian. S0rensen  assumed  91.7  per  cent  dissociation  of  0.1m 
HC1  at  18°C.  Employing  the  same  value  at  25°,  as  an  approxima- 
tion, we  would  find  that  the  hydrogen  electrode  in  0.1m  HC1 
should  be  0.0614  volts  more  negative  than  a  "normal"  hydrogen 
electrode.  If  however  we  take  "the  corrected  concentration  of 
H+  in  0.1m  HC1  as  0.0816"  (Lewis,  Brighton  and  Sebastian)  then 
the  difference  would  be  0.0643.     The  correction  0.0029  should 


STANDARDIZATION    OF   pH   MEASUREMENTS  281 

bring  S0rensen's  value  into  harmony  with  that  of  Lewis,  Brighton 
and  Sebastian.     However,  they  are: 

Lewis,  Brighton  and  Sebastian 0.3357 

S0rensen  (corr.) 0 .  3347 

The  discrepancy  of  0.0010  volt  remains  to  be  explained.  That  it 
may  be  ascribed  partly  to  an  involved  potential  difference  be- 
tween N/10  KC1  and  N/1  KC1  which  has  not  been  noted  in  the 
discussion  and  partly  to  an  excess  correction  for  diffusion  poten- 
tial through  the  use  of  the  Bjerrum  extrapolation  seems  prob- 
able from  the  treatment  accorded  this  subject  by  Fales  and 
Vosburgh;  but  if  we  attempt  to  correct  S0rensen's  data  by  the 
use  of  the  curves  given  by  Fales  and  Vosburgh  the  discrepancy 
noted  above  widens.  It  is  of  no  particular  importance  to  attempt 
further  to  reconcile  the  two  values  because  S0rensen's  original 
data  (1909)  show  wide  variations  in  the  E.  M.  F.s.  of  the  chains 
in  which  hydrochloric  acid  was  used.  One  might  therefore  jump 
to  the  conclusion  that  S0rensen's  value  is  unworthy  of  further 
consideration  now  that  we  have  a  more  probable  value.  It  must 
be  emphasized  however  that  we  are  not  so  much  concerned  with  the 
reliability  of  S0rensen's  original  data  as  we  are  with  the  fact  that 
the  value  thereby  assigned  to  the  tenth  normal  calomel  electrode 
has  been  widely  used  in  the  study  of  hydrogen  electrodes  in  solu- 
tions which  exhibit  comparatively  low  diffusion  potentials  against 
KC1  and  which  furnish  hydrogen  electrode  potentials  reproducible 
with  a  considerable  degree  of  precision.  Because  of  this,  because 
of  the  fact  that  the  S0rensen  value  and  other  comparable  values 
have  standardized  an  enormous  amount  of  biochemical  data  we 
regard  it  as  important  to  consider  the  old  value  further. 

When  S0rensen's  value  has  not  been  used  directly  it  has  been 
used  indirectly  in  the  taking  over  of  pH  values  assigned  to  standard 
solutions  such  as  standard  acetate.  In  Walpole's  study  of  acetate 
mixtures  he  appears  to  have  been  consistent  in  using  the  value 
assigned  by  S0rensen  to  the  tenth  normal  calomel  electrode  referred 
to  the  normal  hydrogen  electrode  under  one  atmosphere  of  hydro- 
gen plus  vapor  pressure.  He  obtained  a  value  for  the  hydrogen 
electrode  potential  in  standard  acetate  agreeing  with  that  found  by 
S0rensen  and  by  Michaelis.  In  Clark  and  Lubs'  study  of  phthal- 
ate,  phosphate  and  borate  buffer  mixtures  they  applied  the  Bjer- 


282  THE   DETERMINATION   OF   HYDROGEN   IONS 

rum  extrapolation,  and,  with  the  qualifications  stated  in  their 
paper  reached  a  value1  for  their  tenth  normal  calomel  electrode 
in  substantial  agreement  with  S0rensen's. 

Palitzsch  doubtless  used  the  S0rensen  value,  which  he  originally 
aided  in  determining,  in  his  study  of  borate  buffer  mixtures. 

A  variety  of  similar  channels  might  be  followed  to,  show  that 
in  the  biochemical  literature  there  is  substantial  agreement  so  far 
as  the  assumed  difference  between  the  tenth  normal  calomel  and 
the  normal  hydrogen  electrodes  is  concerned.  Since  the  liquid 
junction  potential  differences  between  saturated  KC1  and  the 
buffer  solutions  and  physiological  fluids  dealt  with  in  biochemis- 
try are  of  a  low  order  of  magnitude  it  seems  fair  to  assume  that 
the  more  precise  biochemical  data  are  fairly  well  standardized, 
though  not  necessarily  accurate.  The  agreement  was  further- 
more encouraged  in  other  lines  of  investigation  by  the 
recommendation  of  Auerbach  (1912)  when,  in  his  summary  of 
the  work  of  the  "Potential  Commission,"  he  recommended  the 
use  of  the  tenth  normal  calomel  as  a  working  standard  because 
of  its  low  temperature  coefficient,  and  assigned  the  value  0.337 
for  use  between  20°  and  30°. 

On  the  one  hand,  then,  we  have  what  may  be  regarded  as  a 
tacitly  accepted  and  not  yet  precisely  formulated  standardization 
of  the  tenth  normal  calomel  electrode;  and  on  the  other  hand  a 
distinctly  different  value  for  the  tenth  normal  calomel  electrode 
that  is  doubtless  more  nearly  correct,  though  the  details  by  which 
the  value  was  reached  are  not  presented.  The  biochemist  is  thus 
placed  in  an'  embarrassing  position.  Before  making  a  choice  he 
may  consider  the  present  situation  in  our  knowledge  of  the  tem- 
perature coefficients  of  calomel  electrodes. 

In  dealing  with  the  temperature  coefficients  it  will  be  distinctly 
understood  that  we  are  not  concerned  with  the  temperature  co- 
efficient of  the  absolute  difference  of  potential  between  mercury 
and  solution  but  rather  with  the  temperature  coefficient  of  the 
calomel  electrode  in  the  cell:  calomel  electrode-normal  hydrogen 

1  Clark  and  Lubs  give  their  E.  M.  F.'s  reduced  to  refer  to  the  normal 
hydrogen  electrode  under  a  standard  hydrogen  concentration  rather  than 
the  standard  pressure  usually  used.  Since  the  calomel  values  were  also 
referred  to  the  same  basis  the  pH  values  given  by  these  authors  remain  as 
if  the  customary  procedure  had  been  followed. 


STANDAHDIZATION    OF    pH   MEASUREMENTS 


283 


electrode,  when  the  potential  difference  at  the  normal  hydrogen 
electrode  is  defined  to  be  zero  at  all  temperatures.  Unfortunately 
we  have  little  data  upon  this  temperature  coefficient  which  are 
both  accurate  and  extensive.  Therefore  one  who  chooses  to  take 
over  the  better  value  for  the  tenth  normal  or  the  normal  calomel 
electrode  will  still  be  left  in  the  predicament  of  not  knowing  the 
precise  value  to  use  at  temperatures  other  than  25°C. 

We  can  only  reach  approximate  values  in  the  following  manner 
and  compare  the  results  with  comparatively  old  experimental  data. 

Lewis  and  Randall  (1914)  have  derived  a  provisional  tempera- 
ture coefficient  for  the  normal  calomel  electrode  which  indicates 
that  the  values  are  not  a  linear  function  of  the  temperature.  The 
derivation  of  these  authors  as  applied  to  the  tenth  normal  elec- 
trode will  be  followed,  but  some  new  values  obtained  since  the 
writing  of  their  paper  will  be  introduced. 

For  the  cell 


PtH, 


HC1 
0.1  M 


Hg2Cl2  Hg 


Lewis  and  Randall  give  the  empirical  equation 

E  =  0.0964  +  0.001881T  -  0.000,00290^ 

whence 

dE/dT  =  0.001881  -  0.00000580T 

For  present  purposes  this  conforms  closely  enough  with  Ellis' 
(1916)  data. 
It  is  now  assumed  that  the  temperature  coefficient  of  the  cell 


will  apply  to 


PtH, 


PtH2 

HC1 
0.1  M 

Hg5 

I* 

H( 
0.1 

31 
M 

K 
0.1 

CI 
M 

Hg2Cl2  Hg 


if  the  tenth  molar  hydrochloric  acid  calomel  cell  has  the  same 
potential  as  the  tenth  molar  KC1  calomel  cell.  Compare  however 
Lewis,  Brighton  and  Sebastian  (1917)  who  give  0.0012,  and  Mac- 
Innes  (1919)  who  gives  0.0. 


284  THE   DETERMINATION    OF   HYDROGEN   IONS 

For  the  cell 


PtH2 


HC1 
0.1  M 


H+|PtH2 
M 


For  the  cell 

Hg  Hg2Cl2 

KC1 

KC1 

0.1  M 

1.0  M 

Lewis,  Brighton  and  Sebastian  give  0.0644.     Assuming  that  in 
this  cell  the  E.  M.  F.  is  proportional  to  the  absolute  temperature, 

dE 

3^,  =  0.00022.     Hence  for  the  tenth  molar  KC1  calomel  electrode 
ul 

against  the  normal  hydrogen  electrode 

-45  =  0.00166  -  0.00000580T. 
dT 


Hg2Cl2  Hg 


the  author  finds  at  20°  0.0519,  and  at  30°  0.0536.  Interpolation 
between  these  values  on  the  assumption  that  the  E.  M.  F.  is  a 
linear  function  of  the  temperature  gives  an  E.  M.  F.  at  25°  which 
is  within  0.15  millivolts  of  that  found  by  Lewis,  Brighton  and  Se- 
bastian, and  a  linear  temperature  coefficient  of  0.000,17.  Sauer's 
value  at  18°  is  0.0514  and  that  of  Fales  and  Vosburgh  at  25°  is 
0.0524.  Neither  of  these  values  falls  in  with  those  mentioned 
above  but  when  taken  by  themselves  and  with  the  15°  value, 
0.0509,  given  in  the  footnote  of  the  paper  by  Fales  and  Vos- 
burgh (1918)  they  furnish  a  temperature  coefficient  of  the  same 
order. 

With  these  data  we  can  start  from  the  value  0.2828  as  that  of 
the  normal  calomel  electrode  (Lewis,  Brighton  and  Sebastian, 
1917)  at  25°;  or  with  S0rensen's  (1912)  value,  0.3380,  for  the  tenth 
normal  calomel  electrode  at  18°  and  treating  each  set  separately 
we  reach  the  comparisons  shown  in  table  49. 

Bjerrum's  values  at  0°,  25°  and  75°  do  not  fit  in  with  the  calcu- 
lations given  above. 

The  values  given  above  are  admittedly  uncertain  and  are  to  be 
regarded  as  provisional  in  lieu  of  the  experimental  data  that  is 
needed.  It  may  be  emphasized  however  that  there  is  good  reason 
to  believe  that  the  temperature  coefficient  for  the  tenth  normal 
electrode  is  much  lower  than  that  of  the  normal  calomel  electrode. 


STANDARDIZATION    OF    pH   MEASUREMENTS 


285 


Since  we  can  as  yet  only  make  a  good  guess  of  the  temperature 
relations  it  seems  wise  to  choose  as  a  standard  the  calomel  elec- 
trode with  the  smaller  temperature  coefficient  and  thus  lower  one 
chance  of  error.  This  fortunately  has  been,  for  the  most  part, 
the  practice  in  biochemical  work  although  it  runs  counter  to  pref- 
erences which  will  not  be  discussed. 

TABLE  49 


LEWIS 

TENTH 
AGAINST 
NORMAL 
CALOMEL 

S0RENSEN 

t 

1.0  N 

0.1  N 

1.0  N 

0.1  N 

0.1  N 
Found 

18 

0.2844 

^-0.3360 

T 

0.0516 

0.2864 

<-0.3380 

1 

0.3380 

20 

0.2840 

<-0.3359 

T 

0.0519. 

0.2860 

<-0.3379 

1 

0.3378 

25 

0.2828 

— >0.3356 

I 

0.0528 

0.2S48 

<— 0.3376 
I 

30 

0.2817 

«-0.3353 

0.0536 

0.2836 

<-0.3372 

I 

0.3370 

37.5 

0 .  3364 

I 

40 

0  3360 

1 

0.3359 

50 

0  3341 

1 

0.3344 

60 

0.3317 

0.3321 

Approximate  temperature  coefficient  of  normal  calomel  electrode 
-0.000,23. 

Approximate  temperature  coefficient  of  tenth  normal  calomel  electrode 
-0.000,06. 

Let  us  then  assume  that  this  half  cell,  the  tenth  normal  calomel 
electrode,  is  to  be  the  standard  to  which  all  working  electrodes 
are  to  be  referred  and  let  us  consider  finally  the  choice  of  values  to 
be  assigned. 

At  25°C.  the  difference  between  the  values  for  the  tenth  nor- 
mal calomel  electrode  given  in  table  49  is  2  millivolts.  A  change 
of  this  amount  would  shift  the  values  in  the  pH  scale  0.03  unit  pH. 
This  is  quite  insignificant  or  within  the  experimental  error  in  many 
biochemical  studies.  For  certain  purposes  it  is  not  insignificant. 
When  carried  into  mass  action  relations  it  might  be  serious  but 
in  such  relations  there  are  generally  involved  data  taken  over  from 
conductance  measurements.     In  such  a  situation  therefore  there 


286  THE    DETERMINATION    OF   HYDROGEN   IONS 

are  involved  complexities  which  are  by  no  means  covered  by  the 
mere  selection  of  a  more  probable  value  for  the  standard  electrode. 

We  have  already  mentioned  the  fact  that  even  if  the  value  of 
Lewis,  Brighton  and  Sebastian  be  absolutely  correct  at  25°  we 
cannot  assign  accurately  known  values  at  temperatures  other 
than  25°,  and  we  have  noted  the  more  or  less  tacit  assumption  of 
standard  values  for  various  temperatures  in  the  course  of  the 
development  of  biochemical  applications. 

In  addition  to  the  difficulties  mentioned  above  there  is  a  funda- 
mental question  which  runs  throughout  all  present-day  calcu- . 
lations.  As  we  have  reiterated,  all  hydrogen  electrode  measure- 
ments are  referred  by  one  route  or  another  to  some  experimental 
standard  and  the  hydrogen  ipn  concentration  or  hydrogen  ion 
activity,  as  the  case  may  be,  is  estimated  for  this  experimental 
standard  by  the  use  of  theory  which  at  present  is  in  a  state  of 
flux.  One's  inclination  is  to  accept  the  latest  value  advocated 
by  the  most  advanced  thought  and  yet  it  is  an  open  question 
whether  the  inherent  relativity  of  the  whole  subject  will  not  force 
us  ultimately  to  adopt  an  arbitrary  standard.  While  certain 
.investigators  are  accepting  the  value  for  the  normal  calomel  elec- 
trode given  by  Lewis,  Brighton,  and  Sebastian,  Bjerrum  is  apply- 
ing the  theory  of  complete  dissociation  of  salts  and  reaching  a 
very  different  value.  In  the  author's  opinion  it  will  be  wise 
during  the  present  transition  period  to  adopt  a  provisional 
standard  and  in  lieu  of  agreement  reached  in  convention  to  let 
that  standard  be  in  harmony  with  that  tacitly  implied  in  the 
greater  body  of  data.  The  author  therefore  suggests  that  the 
values  in  column  6  of  table  49  be  used  as  provisional  stand- 
ards wherever  there  is  no  definite  reason  to  require  any  other 
value. 

We  can  thus  preserve  uniformity  in  pH  data  and  not  introduce 
ill-considered  changes  which  may  need  subsequent  frequent  re- 
vision before  the  present  theoretical  difficulties  are  removed  or 
before  the  action  of  an  international  committee  fixes  a  standard 
value. 

It  may  be  objected  that  under  such  a  procedure  of  standardiza- 
tion the  symbol  pH  loses  the  precise  significance  which  has  been 

attached  to  it.     It  has  always  been  defined  as  log  — -:.     If   the 


STANDARDIZATION    OF   pH   MEASUREMENTS 


287 


"concentration  chain"  does  not  determine  with  precision  the  ratio 
of  two  hydrogen  ion  concentrations  but  rather  the  ratio  of  two  hy- 
drogen ion  activities,  and  if,  in  addition,  we  adopt  a  standard  of 
reference  in  the  current  use  of  the  hydrogen  electrode  which  is  not 
strictly  true,  then  pH  is  no  longer  expressive  of  the  true  value  of 

log  .    We  need  not  be  concerned  with  the  casuistry  of  this  sit- 

uation.  We  need  only  remember  that  the  more  precise  uses  to 
which  hydrogen  electrode  measurements  may  be  put  involve  the- 
oretical difficulties  which  we  are  not  yet  prepared  in  every  case 
to  deal  with  accurately,2  that  in  the  more  common  uses  the  un- 
certainty is  not  of  a  serious  magnitude  and  that  it  is  preferable 
to  maintain  uniformity  in  the  manner  of  stating  experimental 
values.  If  we  take  care  to  put  a  definite  and  unequivocal  meaning 
to  experimental  data,  relieving  them  as  far  as  possible  from  ill- 
defined  presumptions,  we  majr  be  pardoned  for  continuing  to  use 
in  descriptive  text  and  in  approximate  calculations  "hydrogen 
ion  concentrations."  When  we  come  to  exact  statements  they 
will  be  found  embodied  in  pH  values  of  uniform  experimental 
derivation. 

In  summary  then  it  is  suggested  that : 

1 .  The  following  values  shall  be  taken  as  the  standard  differences 
of  potential,  liquid  junction  potential  differences  being  eliminated, 
between  a  tenth  normal  KCl  calomel  electrode  and  a  hypothetical 
hydrogen  electrode  immersed  in  a  solution  normal  with  respect  to 
the  hydrogen  ions,  under  one  atmosphere  partial  pressure  of 
hydrogen,  and  considered  to  have  zero  difference  of  potential 
between  electrode  and  solution  at  all  temperatures. 


TEMPERATURE 

18° 

20° 

25° 

30° 

37.5° 

40° 

Potential  difference. . 

0.3380 

0.3379 

0.3376 

0.3373 

0.3364 

0  3360 

2.  The  standard  experimental  meaning  of  pH  shall  be  the  cor- 
rected difference  of  potential  between  the  hypothetical  normal 

2  In  very  many  instances  constants  determined  by  conductivity  methods 
are  employed  with  precise  electrode  measurements  without  any  critical 
examination  whatever  of  their  applicability. 


288  THE    DETERMINATION    OF   HYDROGEN   IONS 

hydrogen  electrode  and  the  hydrogen  electrode  under  measure- 
ment (when  this  difference  is  derived  by  the  use  of  the  above 
values),  divided  by  the  numerical  quantity  0.000,198,37  T. 

3.  In  every  case  it  shall  be  specified  whether  the  Bjerrum  ex- 
trapolation with  the  use  of  1.75n  and  3.5n  KC1  was  used  to  elimi- 
nate liquid  junction  potentials  or  whether  saturated  KC1  was  used 
and  considered  to  eliminate  liquid  junction  potentials. 

There  are  those  who  will  prefer  to  use  the  saturated  KC1  calomel 
electrode  as  a  working  standard.  Its  use  eliminates  the  protec- 
tive devices  required  to  guard  the  tenth  normal  calomel  electrode 
against  the  saturated  KC1  used  as  a  liquid  bridge.  Michaelis 
(1914)  has  also  noted  that  its  temperature  coefficient  is  such  that 
it  tends  to  balance  the  effect  of  fluctuations  in  the  temperature  of 
a  calomel  electrode-hydrogen  electrode  chain.  Though  there  are 
involved  in  Michaelis'  reasoning  some  factors  which  are  yet  un- 
certain this  advantage  may  be  granted.  A  practical  system  which 
embodies  the  merits  of  the  saturated  calomel  electrode  and  which 
meets  the  requirements  of  the  standardization  suggested  above  is 
illustrated  on  page  183.  In  this  system  the  saturated  calomel  elec- 
trode is  the  working  standard  whose  value  is  given  by  careful  com- 
parison at  known  temperatures  with  a  set  of  tenth  normal  calomel 
electrodes. 

If  any  ultimate  experimental  standard  other  than  the  tenth 
normal  calomel  electrode  be  used  it  is  suggested  that  for  the 
present  it  be  brought  into  harmony  with  the  above  system,  which 
is  the  system  that  has  practically  governed  past  measurements, 
and  that  fundamental  revision  of  any  standard  await  concerted 
action  based  upon  thorough  investigation  of  both  experimental  and 
theoretical  data. 

These  suggestions  simply  put  into  definite  form  the  current 
procedure  with  the  recognition  on  the  one  hand  that  the  precise 
use  of  electrode  data  involve  many  theoretical  difficulties  and  on 
the  other  hand  that  the  use  of  such  data  for  the  approximate  cal- 
culation of  hydrogen  ion  concentrations  had  best  be  standardized 
for  the  sake  of  uniformity  in  the  records  to  be  handed  on  to  the 
future. 


CHAPTER  XX 
Supplementary  Methods 

When  any  process  has  been  found  to  be  controlled  by  the  con- 
centration of  the  hydrogen  or  hydroxyl  ions,  when  the  quantitative 
relations  have  been  established  and  contributory  factors  are  con- 
trollable, there  is  established  a  possible  means  of  estimating  the 
concentration  of  the  hydroxyl  or  hydrogen  ions.  Many  such  in- 
stances are  known.  From  among  them  a  few  may  be  chosen  for 
their  convenience.  They  are  spoken  of  here  as  supplementary 
methods  because  they  are  superseded  in  general  practice  by  indi- 
cators and  the  hydrogen  electrode.  Several  have  historical  value 
because  they  were  used  in  establishing  the  laws  of  electrolytic 
dissociation.  Others  have  value  because  they  are  available 
either  for  checking  the  customary  procedures  or  for  determina- 
tions in  cases  where  there  is  reason  to  doubt  the  reliability  of  indi- 
cator or  hydrogen  electrode  measurements. 

An  instance  of  the  procedure  outlined  above  is  the  following. 
Clibbens  and  Francis  (1912)  found  that  the  decomposition  of 
nitrosotriacetonamine  into  nitrogen  and  phorone  is  a  function  of 
the  catalytic  activity  of  hydroxyl  ions.  Francis  and  Geake  (1913) 
then  applied  the  relation  to  the  determination  of  hydroxyl  ion 
concentrations,  Francis,  Geake  and  Roche  (1915)  improved  the 
technique,  and  then  McBain  and  Bolam  (1918)  used  the  method 
to  check  their  electrometric  measurements  of  the  hydrolysis  of 
soap  solutions. 

It  is  just  in  such  checking  that  the  value  of  these  so-called  sup- 
plementary methods  will  be  appreciated.  But,  since  they  will  find 
only  occasional  use  and  under  circumstances  which  will  require  a 
detailed  consideration  of  their  particular  applicability,  there 
seems  to  be  no  reason  to  do  more  than  indicate  a  few  of  the  methods 
in  brief  outline. 

THE    QUINHYDRONE    ELECTRODE 

We  have  already  seen  in  Chapter  XVI  that,  when  pH  is  less 
than  about  7,  a  platinum  electrode  in  the  presence  of  hydroqui- 

289 


290  THE    DETERMINATION    OF    HYDROGEN    IONS 

none  and  quinone  should  show  a  potential  difference,  which, 
when  referred  to  the  normal  hydrogen  electrode  as  a  standard 
may  be  expressed  by  the  equation 

RT  ,      RT      [Sdl 

Eh  =  Ek  +  ~y  In  [H+]  -  ^  In  jg-j  (66) 

where  Eh  is  the  observed  single  electrode  potential  difference, 
Etis  a  constant  and  [Sd]  and  [Sq]  are  the  total  concentrations  of 
hydroquinone  and  quinone  respectively.  We  have  also  previously 
noted  that,  under  the  limitations  specified,  Eh  becomes  a  linear 

rs  i 

function  of  pH  when  the  ratio  — ;  is  kept  constant  and  the  tem- 

[bqj 

RT 

perature    is    constant.     (At    30°C,    for   instance,    —  In  [H+]  is 

-  0.06  pH.). 

Now  quinone  and  hydroquinone  combine  in  equimolecular 
proportions  to  form  quinhydrone.  (To  distinguish  this  product 
from  similar  compounds  such  as  that  formed  from  toluenequinone 
and  toluenehydroquinone  it  may  be  called  benzoquinhydrone.) 
In  aqueous  solutions  the  reaction  is  reversible, 

quinone  +  hydroquinone  ^  quinhydrone 

and  since  the  solubilities  are  low,  the  addition  of  solid  quinhy- 
drone is  a  convenient  way  of  providing  a  solution  with  a  mixture 
of  quinone  and  hydroquinone.  We  must  be  careful,  however,  not 
to  assume  that  the  two  are  necessarily  present  in  equimolecular 
concentrations.  We  may  assume  that  the  solid  quinhydrone 
maintains  a  constant  concentration  of  undissociated  quinhydrone 
in  solution.  This  dissociates  and  we  have  the  equilibrium  condi- 
tion where  D  represents  hydroquinone,  Q  quinone  and  QD  quin- 
hydrone: 

[Q][D] 


[QD] 


=  Ki,  and  since  [QD]  is  constant, 


[Q][D]  =  KB,  where  K8  is  the  so-called  solubility  product. 
From  this  it  is  evident  that  only  the  product  [QJ[D]  is  kept  con- 
stant. Ionization  of  D  (hydroquinone)  is  certainly  of  funda- 
mental importance  as  outlined  in  Chapter  XVI  and  we  therefore 
cannot  neglect  to  consider  its  effect  in  the  above  equation.     But 


SUPPLEMENTARY   METHODS  291 

we  have  already  brought  the  electrode  potential  equation  into 
such  a  form  and  simplified  it  with  the  assumption  that  it  is  to 
be  used  in  the  region  of  inappreciable  dissociation  of  D  so  that 
we  are  able  at  once  to  say  that  the  very  slight  ionization  of  the 

rs  i 

hydroquinone  (D)  will  not  appreciably  alter  the  ratio  — — :  from 

IpqJ. 

unity.  Thus  in  acid  solutions  the  presence  of  solid  quinhydrone 
maintains  a  practically  constant,  unit  ratio  of  its  dissociation 
products.  The  last  term  in  equation  (66)  becomes  zero,  and 
we  have 

Eh  =  Ek  -  0.000.198  T  pH  (67) 

When  Ek  has  been  established  a  measurement  of  Eh  enables 
one  to  calculate  pH. 

Biilmann  (1920)  and  Biilmann  and  Lund  (1921)  have  devel- 
oped the  "quinhydrone  electrode"  for  practical  use  and  employ 
the  above  equation,  derived,  however,  in  another  way  (assuming 
the  electrode  to  function  as  an  actual  hydrogen  electrode.  See 
Chapter  XVI). 

For  the  preparation  of  quinhydrone  Biilmann  (1921)  employed 
the  method  of  Valeur.  Later  Biilman  and  Lund  (1921)  found 
it  practicable  to  prepare  the  quinhydrone  as  follows: 

One  hundred  grams  of  ferric  ammonium  alum  in  300  cc.  water 
at  65°C.  is  turned  into  a  warm  solution  of  hydroquinone  in  300 
cc.  water.  The  quinhydrone  precipitates  as  fine  needles.  Cool 
the  mixture  in  ice  and  then  filter  with  suction  washing  the  needles 
three  or  four  times  with  cold  distilled  water.  Yield,  15  to  16 
grams.  It  is  stated  that  the  trace  of  iron  remaining  after  this 
process  is  without  serious  effect. 

To  form  a  "quinhydrone  electrode"  Biilmann  employs  a  vessel 
similar  to  those  used  for  calomel  electrodes  but  with  a  fairly 
large  platinum  electrode  (blank  platinum).  A  little  quinhydrone 
is  mixed  with  the  acid  solution  under  examination,  placed  in 
the  vessel  with  the  platinum  electrode  and  connected  with  a 
saturated  or  other  calomel  electrode. 

Biilmann  determined  Ek  in  equation  (67)  by  simply  fixing  the 
pH  at  a  known  value  with  definite  buffer  solutions  and  measuring 
:he  difference  of  potential  between  a  quinhydrone  electrode  in 


292         THE  DETERMINATION  OF  HYDROGEN  IONS 

this  solution  and  a  hydrogen  electrode  in  the  same  buffer  without 
quinhydrone.     He  gives: 


Temperature 

Ek 

18 

0.704 

25 

0.699 

Besides  the  benzoquinhydrone  electrode  Biilmann  also  describes 
electrodes  formed  with  the  xylene  and  toluene  homologues. 

Biilmann  and  Lund  describe  capillary  vessels  for  use  with 
such  electrodes. 

S0rensen,  S0rensen  and  Linderstr0m-Lang  (1921)  discovered 
that  there  is  a  "salt  error"  with  the  quinhydrone  electrode  which 
becomes  very  appreciable  at  salt  concentrations  of  the  order  of 
M/5.  This  they  ascribe  to  an  altering  ratio  of  activities  for  the 
quinone  and  hydroquinone  with  change  in  salt  content. 

By  methods  for  the  detail  of  which  the  reader  is  referred  to 
the  original  papers  it  is  predicted  that  the  ratio  of  the  activities 
of  hydroquinone  and  quinone  is  defined  when  the  solution  is 
saturated  with  quinhydrone  and  one  of  the  components,  hydro- 
quinone or  quinone;  and  that  under  these  circumstances  there 
should  be  less  "salt  error."  There  may  then  be  formed  what 
Biilmann  and  Lund  call  the  hydro-quinhydrone  electrode  and  the 
quino-quinhydrone  electrode. 

The  hydro-quinhydrone  electrode  is  similar  to  the  quinhydrone 
electrode  described  above  except  that  there  is  present  besides 
solid  quinhydrone,  solid  hydroquinone.  At  18°C.  the  Ek  value 
of  this  electrode  is  given  by  Biilmann  and  Lund  as  0.618. 

In  the  quino-quinhydrone  electrode  there  is  present  besides 
solid  quinhydrone,  solid  quinone.  At  18°C.  the  Ek  value  of  this 
electrode  is  0.756.  In  each  case  the  platinum  of  these  electrodes 
is  positive  to  the  platinum  of  the  hydrogen  electrode  by  the  given 
values. 

There  are  a  number  of  details  in  the  use  of  these  electrodes 
which  require  further  study  and  the  reader  is  referred  to  the  orig- 
inal literature  for  those  which  hrve  already  received  attention. 

Aside  from  the  great  interest  of  the  subject  as  an  example  of 
the  general  relations  pointed  out  in  Chapter  XVI  the  electrodes 
developed  by  the  Danish  investigators  should  be  useful  in  those 
cases  where  the  hydrogen  of  the  hydrogen  electrode  is  seriously 
attacked  by  the  components  of  a  solution.     But  by  the  same  token 


SUPPLEMENTARY   METHODS  293 

the  quinhydrone  electrode  cannot  be  used  when  the  reduction 
potential  of  a  solution  is  such  as  to  seriously  alter  the  ratio  of  the 
hydroquinone  and  quinone.  In  either  case,  however,  there  re- 
mains the  possibility  of  taking  advantage  of  the  slowness  with 
which  some  oxidation-reduction  reactions  come  to  equilibrium 
and  experience  alone  will  indicate  the  limitations  of  usefulness. 
Independently  of  the  Danish  investigations  Granger  and  Nel- 
son (1921)  worked  out  some  of  the  relations  involved  in  the  quin- 
hydrone electrode. 

CONDUCTIVITY 

The  conductivity  of  a  solution  is  dependent  upon  the  concen- 
trations of  all  the  ions  and  upon  the  mobilities  of  each.  It  is 
therefore  obvious  that  a  somewhat  detailed  knowledge  of  the  con- 
stituents of  a  solution  and  of  the  properties  of  the  constituents  is 
necessary  before  conductivity  measurements  can  reveal  any  ac- 
curate information  of  the  hydrogen  or  hydroxyl  ion  concentra- 
tion. Even  when  the  constituents  are  known  it  is  a  matter  of 
considerable  difficulty  to  resolve  the  part  played  by  the  hydrogen 
ions  if  the  solution  is  complex.  However,  the  mobilities  of  the 
hydrogen  and  hydroxyl  ions  are  so  much  greater  than  those  of 
other  ions  (see  page  163)  that  methods  of  approximation  may  be 
based  thereon.  If,  for  instance,  a  solution  can  be  neutralized 
without  too  great  a  change  in  its  composition  it  may  happen  that 
with  the  disappearance  of  the  greater  part  of  the  hydrogen  ions 
there  will  appear  a  great  lowering  in  conductance.  Then,  with 
the  appearance  of  greater  hydroxyl  ion  concentration,  the  conduct- 
ance will  rise.  The  minimum  or  a  kink  in  the  curve  is 
a  rough  indication  of  neutrality.  Thus  the  conductivity  method 
is  sometimes  useful  in  titrations.  See  Kolthoff  for  details  and 
references. 

The  elementary  principles  of  conductivity  measurements  will 
be  found  in  any  standard  text  of  physical  chemistry  but  the  more 
refined  theoretical  and  instrumental  aspects  are  only  to  be  found 
by  following  the  more  recent  journal  literature. 


294 


THE    DETERMINATION    OF   HYDROGEN    IONS 


CATALYTIC   DECOMPOSITION   OF   NITROSOTRIACETONAMINE 

The  reaction  taking  place  is  represented  in  outline  by  the 
following  equation : 

pn/^2  *  C(CH3)2\M  .  ma  _^  nrk/CH:  C(CH3)2   ,   v    ,    w  n 
C0\CH2  •  C(CH3)2/N   N° "*  C0\CH:  C(CH3)2  +  Na  +  Hz° 

The  original  quantity  of  nitrosotriacetonamine  is  known  and  the 
extent  of  the  decomposition  at  the  end  of  measured  intervals  of 
time  is  measured  by  the  volume  of  nitrogen  evolved. 


Fig.  41.  Vessel  for  the  Catalytic  Decomposition  op 
Nitrosotriacetonamine 

Francis,  Geake  and  Roche  (1915)  use  the  vessel  shown  in  figure 
41.  The  tap  of  the  reaction  vessel  contains  a  cup  B  of  7  to  10 
cc.  capacity  into  which  the  alkali  or  the  nitrosoamine  can  be  intro- 
duced through  F.  The  solution  is  then  shut  in  by  turning  the  key 
through  a  right  angle.  The  cup  becomes  a  part  of  the  reaction 
chamber  A  on  turning  the  key  as  shown  in  the  figure.  The  ves- 
sel is  immersed  in  a  thermostat  and  shaken  during  the  whole  ex- 
periment.    The  holes  at  E  and  E'  permit  the  cup  B  to  be  bathed 


SUPPLEMENTARY   METHODS  295 

by  the  thermostat  liquid  and  so  reach  thermal  equilibrium  at  the 
same  time  as  the  chamber  A.  The  tube  R  connects  with  a  con- 
stant volume  burette  where  the  evolved  nitrogen  is  collected  and 
its  pressure  read.  The  tube  D  is  used  for  washing  out  the  vessel 
and  for  filling  it  with  nitrogen  when  the  reaction  has  to  be  con- 
ducted in  an  atmosphere  free  from  oxygen. 

The  unimolecular  equation,  using  the  pressure  method  is 

k  =  2'303  lo     Pc°  ~  P° 
t       °g  P.  -  Pt 

where  P0  is  the  pressure  at  the  time  taken  as  zero,  Pt  the  pressure 
taken  at  the  time  t  and  Poo  the  so-called  infinity  reading  at  the 
end  of  the  experiment.     The  unit  of  time  taken  is  the  second.     At 

30°,  — ^—  =  1.92. 
[OH-] 

It  was  found  that  the  constants  obtained  with  nitrosotriace- 
tonamine  commence  to  drift  when  the  ion  concentration  reaches 
O.Oon  while  at  0.35n  the  drift  ceases  and  the  method  is  again 
applicable.  To  bridge  the  gap  it  was  found  that  nitroso-vinyl- 
and  isobutyl-diacetonamines  could  be  used. 

For  temperature  coefficients  and  for  the  influence  of  neutral 
salts  etc.  the  original  paper  may  be  consulted. 

CATALYTIC    DECOMPOSITION    OF   DIAZOACETIC    ESTER 

Bredig  and  Fraenkel  (1905)  have  described  the  following  reac- 
tion as  applicable  to  the  determination  of  hydrogen  ion  concen- 
trations. 

N2CH.C02  C2H5  +  H20  =  N2  +  (OH)CH2C.C02C2H5 
The  nitrogen  evolved  from  time  to  time  is  measured  and  the 
values  used  in  the  equation 

1  ° 

k  =  „  dn.n  ,  log 


0.4343  t         a  -  x 

vhere  a  is  the  total  gas  at  the  end  of  the  reaction,  x  the  gas  after 

k 
lme  t  minutes  and  k  the  reaction  constant.     At  25°C,  ^r,  =  32.5. 

The  method  was  applied  with  only  partial  success  by  Hober 
1900)  to  blood.  Van  Dam  (1908)  used  it  in  the  examination  of 
ennet  coagulation  of  milk. 


296  THE    DETERMINATION    OF   HYDROGEN    IONS 

THE   INVERSION  OF    CANE    SUGAR 

This  has  been  a  favorite  subject  of  study  by  those  interested 
in  the  catalytic  activity  of  the  hydrogen  ion.  It  has  been 
used  in  a  number  of  instances  for  the  determination  of  the 
hydrogen  ion  concentration  of  biochemical  solutions,  but,  like 
all  catalytic  processes,  its  close  study  has  revealed  a  number  of 
complicating  factors  which  necessitate  the  greatest  caution  in  the 
interpretation  of  results. 

So  numerous  are  the  papers  dealing  with  sugar  hydrolysis  by 
acid  that  the  reader  is  referred  to  the  very  thorough  review  by 
Woker  for  the  older  work.  For  the  more  recent  investigations 
see,  for  example,  Jones  and  Lewis,  1920. 

CATALYSES    IN   GENERAL 

Pending  further  development  of  the  theory  of  strong  electrolytes 
and  of  the  "salt  effect",  the  investigator,  using  one  or  another 
of  the  above  catalysis  methods  merely  as  a  check,  can  place  his 
data  upon  a  reproducible  basis  by  using  the  following  system  of 
comparison.  Determine  the  pH  values  of  a  series  of  buffer 
solutions  lying  within  the  pH  range  expected  of  the  unknown, 
and  having  total  salt  concentrations  comparable  to  that  of  the 
solution  to  be  tested.  Under  parallel  conditions  determine  the 
catalytic  activity  of  knowns  and  unknown.  Assume  that  the 
result  with  the  buffer  agreeing  closest  to  that  of  the  unknown 
indicates  that  this  buffer  and  the  unknown  are  at  the  same  pH 
and  check  by  various  modifications  of  buffer. 

MISCELLANEOUS   METHODS 

Were  it  worth  while  there  could  be  compiled  under  this  heading 
a  wide  variety  of  phenomena  which  have  actually  been  used  to 
determine  approximately  the  hydrogen  ion  concentration  of  a 
solution.  We  may  instance  the  precipitation  Of  casein  from  milk 
by  the  acid  fermentation  of  bacteria.  This  has  not  been  clearly 
distinguished  in  all  cases  from  coagulation  produced  by  rennet- 
like enzymes;  but,  when  it  has  been,  the  precipitation  or  non-pre- 
cipitation of  casein  from  milk  cultures  has  served  a  useful  purpose 
in  the  rough  classification  of  different  degrees  of  acid  fermentation. 


SUPPLEMENTARY    METHODS  297 

In  like  manner  the  precipitation  of  uric  acid  or  of  xanthine  has 
been  used  (Wood,  1903). 

The  alteration  of  the  surface  tension  of  solutions  (Windish  and 
Dietrich,  1919-1921),  the  distillation  of  ammonia  (Vely  1905),  dis- 
tribution ratios  between  different  solvents,  and  various  other 
methods  have  been  used  to  furnish  data  for  the  estimation  of 
hydrogen  or  hydroxyl  ion  concentrations. 


CHAPTER  XXI 

Applications 

Finally,  acidity  and  alkalinity  surpass  all  other  conditions,  even 
temperature  and  concentration  of  reacting  substances,  in  the  influence 
which  they  exert  upon  many  chemical  processes. — L.  J.  Henderson. 

It  is  because  of  the  great  variety  of  applications  in  research, 
routine  and  industry  that  the  theories  and  devices  outlined  in  the 
previous  chapters  have  been  developed.  The  physical  chemist 
sees  in  them  the  instruments  of  approximation  or  of  precision 
with  which  there  have  been  discovered  orderly  relations  of  ines- 
timable service  to  the  analyst  and  with  which  there  have  been 
established  quantitative  values  for  affinity  or  free  energy.  The  bio- 
chemist might  almost  claim  some  of  these  methods  as  his  own,  not 
only  because  necessity  has  driven  him  to  take  a  leading  part  in 
their  development,  but  also  because  their  application  has  become 
part  of  his  daily  routine  in  very  many  instances. 

As  mentioned  in  the  preface  to  the  first  edition  the  applications 
have  become  so  numerous  and  in  many  cases  so  detailed  that  the 
time  has  come  for  a  redispersion  among  the  several  sciences  of 
the  material  that  has  from  time  to  time  been  grouped  about  the 
activity  of  the  hydrogen  ion.  This  chapter  therefore  is  written 
only  as  a  cursory  review  with  the  hope  that  it  may  be  of  service 
to  the  student  by  revealing  the  interdependence  of  specialized 
lines  of  research,  by  suggesting  how  mistakes  still  current  have 
been  eliminated  by  those  who  realize  the  importance  of  the  sub- 
ject and  by  furnishing  a  rough  index  to  our  incomplete  bibliog- 
raphy of  a  voluminous  literature. 

In  the  compilation  of  the  bibliography,  of  which  this  chapter 
constitutes  an  index,  no  attempt  has  been  made  to  include  all  of 
the  very  numerous  instances  in  which  the  activity  of  the  hydrogen 
or  the  hydroxyl  ions  has  been  found  to  influence  the  course  of  spe- 
cific chemical  reactions,  such  as  the  hydrolysis  of  polysaccharides, 
special  oxidations  and  condensations,  or  the  nature  and  accuracy 
of  the  numerous  color  tests  used  for  the  qualitative  recognition  of 
special  chemical  groupings.     The  reader  will  find  in  Woker's  ex- 

298 


APPLICATIONS  299 

tensive  monograph,  Die  Katalyse,  not  only  a  very  complete  re- 
view of  the  older,  widely  scattered  literature  upon  these  aspects 
of  hydrogen  and  hydroxyl  ion  activity  but  also  an  abundance  of 
material  which  still  remains  to  be  reworked  with  the  more  modern 
methods. 

In  the  classification  of  the  bibliography  no  attempt  has  been 
made  to  place  the  references  in  strictly  logical  catagories,  nor 
has  it  been  practical  to  make  a  minute  subdivision  by  subjects 
with  numerous  cross  references.  The  grouping  is  by  subjects 
which  are  of  particular  current  or  historical  interest  or  which 
fall  within  the  provinces  of  special  branches  of  science. 

General  Reviews.  Excellent  general  reviews  of  biochemical 
applications  are  S0rensen's  article  in  Ergebnisse  der  Physiologie, 
1912,  and  MichaekV  monograph  Die  W  asserstoffionenkonzentra- 
tion,  1914.  As  we  go  to  press  there  comes  to  hand  the  first  part 
of  the  1922  revised  edition  of  this  excellent  monograph.  This 
first  part  covers  in  extended  form  the  theoretical  foundations 
briefly  treated  in  the  first  edition  and  deals  in  more- or  less  detail 
with  many  subjects  briefly  touched  upon  in  the  following  pages. 
Prideaux  has  compiled  a  great  deal  of  valuable  data  in  The  Theory 
and  Use  of  Indicators,  London,  1917.  In  this  English  work  will 
be  found  the  more  important  matter  which  Bjerrum  (1914) 
embodied  in  his  monograph  on  the  theory  of  titration  and  which 
Noyes  had  previously  summarized  in  his  paper  "Quantitative 
application  of  the  theory  of  indicators  to  volumetric  analysis," 
(1910).  The  analyst  will  find  a  wealth  of  helpful  suggestions  in 
Stieglitz'  Qualitative  Analysis.  A  review  of  the  indicator  method 
which  is  of  some  general  interest,  although  written  specially  for 
the  bacteriologist,  will  be  found  in  The  Journal  of  Bacteriology, 
2,  nos.  1,  2  and  3  (Clark  and  Lubs,  1917). 

Those  who  desire  to  review  the  theory  of  electrolytic  dissociation 
with  special  reference  to  its  bearing  on  electrode  measurements 
will  find  useful  LeBlanc's  Text  Book  of  Electrochemistry  (1907). 

Among  several  papers  which  may  be  called  classics  in  biochem- 
istry there  will  be  recognized  the  preeminence  of  S0rensen's  Etudes 
enzymatiques,  II,  from  the  Carlsberg  Laboratory  in  Copenhagen 
and  Das  Gleichgewicht  zwischen  Basen  und  Sduren  im  tierischen 
Organismus  by  Henderson  of  Harvard. 

The  Theory  of  Titration  is  so  closely  allied  with  the  more 


300         THE  DETERMINATION  OF  HYDROGEN  IONS 

general  applications  of  indicators  and  the  hydrogen  electrode  that 
it  may  well  be  taken  from  the  alphabetic  arrangement  to  be  fol- 
lowed and  treated  before  taking  up  some  general  considerations. 

The  stress  which  has  come  to  be  laid  upon  that  factor  of  "acid- 
ity" with  which  we  have  been  dealing  should  not  detract  from  the 
true  importance  of  the  estimation  of  total  acidity  or  alkalinity  by 
titration. 

But  the  theory  of  titration  is  only  a  special  form  of  the  theory 
with  which  we  have  been  concerned  up  to  this  point;  so  that  we 
are  prepared  to  sketch  in  outline  those  salient  features  of  the  well- 
ordered  theory  which  has  displaced  the  loose  empiricism  of  other 
days. 

In  figure  42  are  shown  the  titration  curves  of  hydrochloric, 
acetic  and  boric  acids,  determined  as  outlined  in  Chapter  II.  The 
ordinates  of  figure  42  are  pH  values  and  the  abscissas  cubic  centi- 
meters of  N/10  NaOH  added  to  10  cc.  N/10  acid.  At  the  side 
of  the  main  part  of  the  figure  are  representations  of  the  color  trans- 
formations of  two  indicators  (see  Chapter  IV). 

Although  the  indicator  curves  are  drawn  at  one  side  of  the  figure 
the  reader  will  readily  see  from  the  theory  described  in  Chapter 
IV  that  they  could  have  been  placed  in  the  main  figure  parallel 
to  the  titration  curves  if  the  abscissas  had  been  made  percentage 
neutralization. 

A  more  complete  picture  of  the  conditions  of  titration  would 
be  shown  had  the  curves  been  extended  to  indicate  what  happens 
when  the  "end-points"  are  overstepped.  The  reader  may  pic- 
ture this  for  himself  by  imagining  that  the  curve  for  boric  acid 
continues  with  the  slope  shown  at  11  and  then  flattens  out  be- 
tween 12  and  13,  and  that  the  other  curves,  after  passing  pH  10, 
sweep  to  the  right  to  join  the  extended  boric  curve. 

When  all  but  a  very  small  part  of  the  hydrochloric  acid  has  been 
neutralized  there  comes  a  sharp  break  in  the  titration  curve.  On 
the  addition  of  the  last  trace  of  alkali  required  for  complete  neu- 
tralization the  pH  of  the  solution  plunges  to  the  alkaline  region. 
In  this  precipitous  change  the  pH  passes  the  range  of  methyl  red, 
and,  with  an  amount  of  alkali  that  will  be  detected  only  by  careful 
observation,  it  passes  into  that  range  of  pH  where  phenolphthalein 
shows  its  various  degrees  of  color.  Therefore,  with  the  exclusion 
of  carbon  dioxid,  either  indicator  may  be  used  to  indicate  the  "end 


APPLICATIONS 


301 


point"  of  this  titration.  The  case  is  very  different  in  the  titration 
of  acetic  acid.  Here  we  have  an  acid  whose  dissociation  constant 
(see  Chapter  I)  is  so  low  that  the  flat  portion  of  the  titration  curve 
lies  in  that  region  of  pH  where  methyl  red  shows  its  various  de- 


1 

2 
3 

A 

• 

^CV 

5 
6 

7 

8 

9 

10 
pH 

^<^c 

4£rr> 

^^ 

4£*d 

i 

I         A 

1.      t 

>      I 

i     1 

0 

Fig.  42.  Titration  Curves  of  10  cc.  N/10  Acids  with  N/10  NaOII 


302  THE    DETERMINATION    OF   HYDROGEN   IONS 

grees  of  color.  In  other  words  the  apparent  dissociation  constant 
of  methyl  red  is  not  far  from  that  of  acetic  acid.  Therefore,  as 
the  titration  of  acetic  acid  proceeds,  and  long  before  the  neutraliza- 
tion of  the  acetic  acid  is  complete,  methyl  red  has  been  partially 
transformed  and  at  last  is  so  extensively  transformed  that  no 
marked  change  of  color  is  observed  when  the  pH  of  the  solution 
abruptly  changes  with  complete  neutralization  of  the  acetic  acid. 
It  is  at  once  evident  why  an  indicator  with  the  properties  of 
phenolphthalein  must  be  used  in  such  a  case.  In  the  titration  of 
a  still  weaker  acid,  such  as  boric  acid,  phenolphthalein  becomes 
comparable  to  methyl  red  in  the  latter's  conduct  in  acetate  solu- 
tions. To  titrate  boric  acid  it  must  be  combined  with  glycerine 
or  mannitol  to  form  a  stronger  acid.     See  Liempt  (1920). 

The  titration  curve  of  boric  acid  is  representative  of  the  conduct 
of  many  of  the  weak  acidic  groups  found  in  the  substances  of 
biochemical  interest. 

Sometimes  by  a  judicious  selection  of  indicators  it  is  possible  to 
titrate  in  succession  a  mixture  of  two  acids.  For  instance  A.  B. 
Clark  and  Lubs  (1918)  have  called  attention  to  the  advantages  of 
the  two  color  transformations  of  thymol  blue.  The  color  trans- 
formation of  thymol  blue  in  the  acid  range  is  such  that  it  may  be 
used  to  indicate  the  approximate  end  point  of  hydrochloric  acid 
in  the  presence  of  acetic  acid ;  and  the  second  color  change  occurs 
in  a  region  of  pH  such  that  it  will  indicate  the  end  point  in  the 
titration  of  the  acetic  acid.  A.  B.  Clark  and  Lubs  (1918)  and  Lubs 
(1920)  have  examined  other  similar  uses  of  this  indicator. 

The  principles  thus  briefly  outlined  apply  to  the  titration  of 
bases  with  strong  acids,  but,  of  course,  with  the  direction  of  pH 
change  reversed  and  with  the  end  points  tending  to  He  on  the  acid 
side  of  pH  7.0.  A  hydrogen  ion  concentration  of  10_7n  or  pH  7.0 
is  called  the  neutral  point  because  it  is  the  concentration  of  both 
the  hydrogen  and  the  hydroxyl  ions  in  pure  water;  but  it  is  evi- 
dently seldom  the  practical  or  even  the  theoretical  point  of  neu 
trality  for  titrations. 

As  phenolphthalein  is  the  more  generally  useful  indicator  for 
the  titration  of  acids  with  strong  bases  so  is  methyl  red  the  more 
generally  useful  indicator  in  the  titration  of  bases  with  strong  acids. 
Each  fails,  however,  when  the  acid  or  base  is  very  weak,  and  each 
may  be  replaced  by  a  more  suitable  indicator  in  special  cases. 


APPLICATIONS  303 

For  the  treatment  of  these  cases  the  reader  should  consult  the 
detailed  description  of  the  theory  of  titration  in  one  of  the  papers 
mentioned  above. 

Where  high  color  or  turbidity  interferes  with  the  use  of  indi- 
cators in  titration  the  hydrogen  electrode  is  often  useful.  See 
Bottger  (1897),  Hildebrand  (1913)  Michaelis  (1917).  Since  it 
may  be  necessary  only  to  detect  the  "break"  in  the  titration  curve, 
the  hydrogen  electrode  system  and  potentiometer  system  used  for 
this  purpose  may  be  very  simple.  The  hydrogen  electrode  has 
the  advantage  that  it  may  often  be  used  where  colorimetric  tests 
are  impracticable  and  that  it  may  be  linked  electrically  with  auto- 
matic regulating  and  recording  instruments  such  as  Leeds  and 
Northrup  Company  have  devised  for  industrial  use. 

Pinkhof  (1919)  has  suggested  special  half-cells  with  single 
potentials  equal  to  those  of  the  end-points  of  titrations,  thereby 
eliminating  the  necessity  of  a  potentiometer.  A  galvanometer 
or  electrometer  indicates  equalization  of  potentials  and  hence  the 
attainment  of  the  "end-point." 

In  like  manner  one  may  use  two  hydrogen  electrodes  as  de- 
scribed in  Chapter  IX.  If  one  electrode  is  immersed  in  a  solu- 
tion having  the  pH  of  the  desired  end-point,  the  attainment  of 
this  end-point  in  the  other  solution  is  indicated  by  the  point  of 
reversal  of  current  in  the  galvanometer  (Klopsteg,  1921). 

Since  titrimetric  determination  of  total  acidity  or  basicity 
involves  one  or  another  method  of  estimating  pH,  the  under- 
standing of  the  principles  involved  is  essential  to  an  intelligent 
interpretation  of  the  values  obtained  in  the  titration  of  complex 
mixtures.  In  a  great  many  instances  there  have  been  carried 
over  to  the  titration  of  complex  mixtures  the  rule-of-thumb  method 
and  the  special  interpretation  first  worked  out  by  the  analyst  for 
the  titration  of  strong  acids  and  bases.  Now  it  not  infrequently 
occurs,  especially  among  extracts  of  natural  products,  that  there 
are  present  a  variety  of  weak  acids  and  bases;  and  no  precipitous 
drop  in  the  titration  curve  can  be  observed  in  the  pH  zones  covered 
by  the  indicators  very  generally  employed  in  such  titrations. 
The  situation  is  comparable  with  an  attempt  to  titrate  boric  acid 
with  phenolphthalein  as  indicator.  No  sharp  "end-point"  is 
observable.  But  there  will  always  remain  the  distinctive  value 
of  a  titration  and  wherever  this  cannot  be  precisely  analyzed  it 
should  be  stated  in  simple  straightforward  terms. 


304  THE    DETERMINATION    OF   HYDROGEN   IONS 

In  the  majority  of  cases  the  titration  of  such  solutions  reduces  to  a  mere 
revelation  of  differences  in  total  buffer  action  furnishing  but  one  definite 
point  on  the  titration  curve.  The  procedure  often  followed  is  comparable 
with  the  practice  of  the  ancient  Romans  who,  according  to  Trillat  (1916), 
(cf.  Stephanides  1916)  titrated  natural  waters  with  drops  of  red  wine. 
While  modern  standards  of  concentration  are  more  exact  than  the  wine 
standard  of  the  Romans  their  significance  is  largely  lost  by  a  choice  of  in- 
dicators as  accidental  as  the  Roman  choice  of  the  coloring  matter  of  red 
wine.  The  frank  admission  that  the  content  of  acids  in  some  complex 
solutions  cannot  be  determined  by  titration  need  not  destroy  the  value 
of  the  information  gained  by  a  titration  if  this  information  be  correctly 
used.  But  too  often  the  matter  is  carried  to  an  extreme.  In  the  routine 
methods  for  titrating  milk  a  perfectly  simple  test  has  been  so  elaborated 
that  it  not  only  has  become  confusing  to  the  chemist  but  so  misleading  to 
the  creamery  man  that  it  is  causing  large  economic  losses.  Often  the 
initial  pH  of  a  solution  is  of  greater  significance  than  is  the  titration  value 
obtained  after  juggling  the  solution  with  acid  or  alkali.  Illustrations  of 
this  are  to  be  found  in  the  author's  treatment  of  bacteriological  culture 
media  (Clark,  1915). 

Having  followed  some  of  the  salient  features  of  titration  and 
found  this  procedure  linked  with  the  more  general  aspects  of  hy- 
drogen ion  determinations  the  reader  is  reminded  of  those  relations 
among  acids  and  bases  outlined  in  Chapter  I  which  point  to 
certain  general  considerations. 

General  Considerations.  As  a  comprehensive  generaliza- 
tion it  may  be  said  that  the  hydrogen  ion  concentration  of  a  solu- 
tion influences  in  some  degree  every  substance  with  acidic  or  basic 
properties.  When  we  have  said  this  we  have  said  that  the  hydro- 
gen ion  concentration  influences  the  great  majority  of  compounds, 
especially  those  of  biochemical  interest.  Such  a  generalization, 
however,  would  be  misleading  if  not  tempered  by  a  proper  appreci- 
ation of  proportion.  Rarely  is  it  necessary  to  consider  the  ioniza- 
tion of  the  sugars  since  their  dissociation  constants  are  cf  the  order 
of  10~13  and  their  ionization  may  be  generally  neglected  in  the  pH 
region  usually  encountered  in  physiological  studies.  Likewise 
there  are  zones  of  pH  within  which  any  given  acidic  or  basic  group 
will  be  found  in  dilute  solution  to  be  in  a  practically  undissociated 
or  fully  dissociated  state.  Perhaps  there  is  no  more  vivid  way  of 
illustrating  this  than  by  a  contemplation  of  the  conduct  of  indi- 
cators. Above  a  certain  zone  of  hydrogen  ion  concentration 
phenolphthalein  solutions  are  colorless.     Below  this  zone  (until 


APPLICATIONS  305 

intense  alkalinity  is  reached)  only  the  colored  form  exists.  Within 
the  zone  the  virage  of  a  phenolphthalein  solution  is  intimately 
related  to  the  hydrogen  ion  concentration.  The  conduct  of  phen- 
olphthalein, which  happens  to  be  visible  because  of  tautomeric 
changes  which  accompanj^  dissociation,  is  a  prototype  of  the  con- 
duct of  all  acids.  Just  as  we  may  suppress  the  dissociation  of 
phenolphthalein  by  raising  the  hydrogen  ion  concentration  of  the 
solution  so  may  we  suppress  the  dissociation  of  any  acid  if  we  can 
find  a  more  intensely  ionizing  acid  with  which  to  increase  the  hy- 
drogen ion  concentration  of  the  solution.  Similar  relations  hold 
for  bases,  and,  if  we  regard  methyl  red  as  a  base,  we  may  illustrate 
with  it  the  conduct  of  a  base  as  we  illustrated  the  conduct  of  an 
acid  by  means  of  phenolphthalein. 

Such  illustrations  may  serve  to  emphasize  the  reason  underly- 
ing the  following  conclusion.  Whenever,  in  the  study  of  a  physi- 
ological process,  of  a  step  in  analysis  requiring  pH  adjustments  or 
of  any  case  involving  equilibria  comparable  with  those  mentioned 
above,  there  is  sought  the  effect  of  the  pH  of  the  solution,  it  may 
be  expected  that  no  particularly  profound  effect  will  be  observed 
beyond  a  certain  zone  of  pH.  Within  or  at  the  borders  of  such  a 
zone  the  larger  effects  will  be  observed.  From  this  we  may  con- 
clude that  the  methods  of  determining  hydrogen  ion  concentra- 
tions should  meet  two  classes  of  requirements.  In  the  first  place, 
when  the  phenomenon  under  investigation  or  control  involves  an 
equilibrium  which  is  seriously  affected  by  the  pH  of  the  solution, 
the  method  of  determining  pH  values  should  be  the  most  accurate 
available.  In  the  second  place,  when  the  equilibrium  is  held  prac- 
tically constant  over  a  wide  range  of  pH,  an  approximate  deter- 
mination of  pH  is  sufficient  and  refinement  may  be  only  a  waste 
of  time. 

Neglecting  certain  considerations  which  often  have  to  enter  into 
a  choice  of  methods  it  may  be  said  that  the  electrometric  method 
had  best  be  applied  in  the  first  case  and  the  indicator  method  in 
the  second.  When  the  nature  of  the  process  is  not  known,  and  it 
therefore  becomes  impossible  to  tell  a  priori  which  method  is  to  be 
chosen,  the  colorimetric  method  becomes  a  means  of  exploration 
and  the  electrometric  method  a  means  of  confirmation. 

Exception  will  be  taken  to  this  statement  as  comprehensive 
for  there  are  cases  where  one  or  the  other  method  has  to  be 


306  THE    DETERMINATION    OF   HYDROGEN   IONS 

discarded  because  of  the  nature  of  the  solution  under  examina- 
tion. Nevertheless,  in  general,  the  utility  of  the  colorimetric 
method  lies  in  its  availability  where  approximations  are  needed  and 
exact  determinations  are  useless  and  also  in  its  value  for  recon- 
naissance; while  the  value  of  the  electrometric  method  lies  in  its 
relative  precision. 

In  some  instances  the  qualitative  and  quantitative  relations  of 
a  phenomenon  to  pH  should  be  carefully  distinguished.  Note,  for 
instance,  the  significance  of  an  optimum  or  characterizing  point. 
Consider  the  conduct  of  phenol  red  and  of  cresol  red.  These  two 
indicators  appear  to  a  casual  observer  to  be  very  much  alike  in 
color  and  each  exhibits  a  similar  virage  in  buffer  solutions  of  pH 
7.6,  7.8,  etc.  Careful  study,  however,  shows  that  each  point  on 
the  dissociation  curve  of  phenol  red  lies  at  a  lower  pH  than  the  cor- 
responding point  on  the  dissociation  curve  of  cresol  red.  If  the 
half  transformation  point  be  taken  as  characteristic  it  may  be 
used  to  identify  these  two  indicators.  Likewise  it  is  the  dissocia- 
tion constant  of  an  acid  or  a  base,  the  isoelectric  point  of  a  protein, 
the  optimum  pH  for  acid  agglutination  of  bacteria,  or  an  optimum 
for  a  process  such  as  enzyme  activity  that  furnishes  characteristic 
data. 

When  there  is  observed  a  correlation  between  pH  and  some  effect, 
the  mere  determination  of  pH  alone  will  of  course  throw  but  little 
light  upon  the  real  nature  of  the  phenomenon  except  in  rare  in- 
stances. Determination  of  the  hydrogen  ion  concentration  will 
not  even  distinguish  whether  a  given  effect  is  influenced  by  the 
hydrogen  or  the  hydroxyl  ions,  nor  will  it  always  reveal  whether 
the  influence  observed  is  direct  or  indirect.  It  is  true,  however, 
that,  even  when  the  hydrogen  ion  concentration  is  effective 
through  remote  channels,  it  may  be  very  important.  Therefore 
advantage  should  be  taken  of  the  comparative  ease  with  which  the 
concentration  of  hydrogen  ions  may  be  determined  or  controlled 
and  its  influence  known  or  made  a  constant  during  the  study  of 
any  other  factor  which  may  influence  a  process.  From  this 
point  of  view  methods  of  determining  hydrogen  ion  concentration 
take  their  place  beside  thermometers,  and  buffer  mixtures  beside 
thermostats. 

Indeed  it  may  be  said  that  the  failure  to  take  advantage  of 
buffers  is  still  a  prolific  source  of  error  in  the  experimental  work 


APPLICATIONS  307 

of  every  branch  of  science  having  to  do  with  solutions.  In  one 
case  the  neglect  is  gross;  in  another  case  it  may  be  a  perfectly 
excusable  misjudgment.  A  complete  understanding  of  the 
effects  of  the  hydrogen  or  hydroxyl  ion  is  very  far  from  attainment 
and  those  who  faithfully  control  the  pH  of  their  solutions  are 
often  rewarded  by  the  most  surprising  results.  To  emphasize 
this  aspect  we  may  call  attention  to  the  fact  that  while  the  disso- 
ciation of  glucose  is  quite  negligible  in  the  region  of  pH  7  so  far 
as  any  appreciable  effect  upon  the  displacement  of  other  acid- 
base  equilibria  is  concerned,  the  converse  proposition  is  decidedly 
not  negligible.  A  shift  in  pH  from  7.0  to  7.4  has  a  very  marked 
influence  upon  the  conduct  of  glucose  in  heated  solutions  as  every 
media  maker  knows.  Nor  may  it  be  forgotten  that  there  are  many 
compounds  only  the  main  dissociation  constants  of  which  have 
been  determined;  until  we  know  the  values  of  secondary  acidic 
or  basic  dissociations,  we  have  not  a  complete  description  upon 
which  to  base  judgment  of  the  conduct  of  such  compounds  in 
relation  to  pH. 

It  is  the  opinion  of  the  author  that  altogether  too  much  em- 
phasis has  been  placed  upon  the  so-called  "neutral  point."  The 
relation  [H+]  [OH]  =  Kw  holds  all  along  the  scale.  The  equality 
[H+]  =  [OH]  or  pH  =  pOH  occurs  at  pH  7.  This  is  a  convenient 
reference  point  and  has  been  seized  upon  as  the  point  of  division 
in  our  habitual  ideas  of  "acidity"  and  "alkalinity."  But 
pH  7  is  not  used  as  the  end  point  in  titrations,  it  is  not  the  neutral 
point  in  the  conduct  of  ampholytes  or  selectively  adsorbing  ma- 
terial, and  seldom  is  anything  unique  seen  to  happen  when  in  a 
series  of  experiments  a  solution  "crosses  the  line." 

Living  cells  are  dependent  upon  the  maintenance  of  a  strictly 
limited  hydrogen  ion  concentration  in  their  environment.  The 
recognition  of  this  as  a  fact,  independently  of  any  theory  whatever 
regarding  the  channels  of  influence,  has  brought  hydrogen  ion 
methods  into  the  culture  laboratory  and  into  the  garden.  Accus- 
tomed as  we  are  to  dealing  with  ponderable  quantities  of  material 
we  are  sometimes  startled  by  the  fact. that  a  cell  is  dependent 
upon  the  maintenance  of  an  environment  varying  between  the 
limits  0.000,001  and  0.000,000,01  gram  hydrogen  ions  per  liter. 
Sometimes  the  permissible  limits  are  even  closer  but  the  order  of 
magnitude  remains  the  same.     Such   values,   however,  do  not 


308  THE    DETERMINATION    OF   HYDROGEN    IONS 

represent  entities  separable  from  the  other  material  present  in 
solution.  They  represent  only  a  position  of  balance  among  rela- 
tively large  quantities  of  material  containing  a  reserve  of  potential 
hydrogen  ions. 

Now  that  N,  the  number  of  molecules  of  solute  present  per 
litre  in  a  molar  solution,  is  accurately  known  (Millikan),  it  is 
certain  that  even  in  a  solution  having  a  hydrogen  ion  normality 
as  low  as  10-13  there  are  about  1010  hydrogen  ions  per  litre.  This 
estimate,  when  taken  in  conjunction  with  the  electrical  charge 
associated  with  each  ion,  may  indicate  how  it  is  that  a  normality 
of  10-13  H+  may  be  detected. 

But  there  still  remains  the  fact  that  this  normality  is  very  low 
in  comparison  with  the  other  material  present  even  in  distilled 
water.  In  solutions  heavily  buffered  at  pH  13  we  find  the  hydro- 
gen electrode  or  an  acid  indicator  rigidly  stabilized  in  its  conduct 
and  it  is  questioned  whether  this  can  be  brought  about  by  such 
extreme  relative  dilutions  of  the  hydrogen  ions  alone.  Keller 
(1921)  has  expressed  doubt  of  another  sort.  He  calls  attention 
to  the  diminutive  size  of  the  hydrogen  ion  (allowing  for  hydration) 
compared  with  a  giant  protein  molecule,  and,  picturesquely  pro- 
portioning the  one  to  the  other  as  a  bacterium  to  a  Mont  Blanc, 
he  questions  the  influence  upon  the  protein  which  is  attributed 
to  the  hydrogen  ion. 

All  these  are  "sharp-toothed  questions"  which,  were  they 
"baited  with  more  skill,  needs  must  catch  the  answer."  In  many 
of  the  answers  given,  however,  there  lies  an  easily  detected  fallacy. 
Our  present  convenient  modes  of  formulating  relations  are  regarded 
as  complete  pictures  of  the  physical  facts  and  as  such  are  followed 
to  the  bitter  end  with  disastrous  results.  In  a  previous  chapter 
we  have  attempted  to  broaden  the  outlook  just  a  little,  and  have 
suggested  that  in  many  cases  a  more  complete  formulation  of 
relations  would  show  that  as  the  physical  effectiveness  of  one  ion 
fades  out  at  extreme  dilution  other  components  of  the  solution 
maintain  the  continuity.  From  this  point  of  view  even  the  more 
extreme  "calculation  values"  retain  a  definite  significance. 

In  like  manner  an  extreme  hydrogen  ion  concentration  may  be 
significant  as  an  index  of  the  state  of  an  equilibrium  with  which 
the  hydrogen  ion  itself  has  little  actual  physical  significance.  Its 
introduction  as  a  component  of  the  equilibrium  is  a  convenient 


APPLICATIONS  309 

and  at  the  same  time  a  stoichiometrically  true  and  mathemati- 
cally correct  mode  of  expression  containing  no  implications  re- 
garding the  actual  physical  effectiveness  of  a  small  hydrogen  ion 
concentration  as  an  individual  quantity  separable  from  the  other 
components  of  a  solution.  At  higher  concentrations  there  can 
be  little  doubt  of  the  physical  effectiveness  of  the  hydrogen  ions 
whatever  their  size,  or  energy  relative  to  other  bodies.  The 
energy  placed  on  the  grid  of  an  electron  tube  may  be  small,  but 
the  potential  of  the  grid  may  determine  a  large  flow  of  energy 
between  filament  and  plate.  The  hydrogen  ions  in  a  solution 
may  be  small  in  relative  size  or  relative  numbers,  but  they  may 
control  the  mobilization  of  a  large  reserve.  If  one  seeks  to  go 
further,  perhaps  to  formulate  a  more  fundamental  basis,  he  still 
has  to  conform  to  the  experimental  data  at  hand. 

These  data  are  too  extensive,  too  detailed  and  altogether  too 
complete  to  admit  any  doubt  of  the  pragmatic  value  of  those 
measurements  we  now  customarily  express  in  terms  of  hydrogen 
ion  concentration  or  activity.  Such  values  do  indicate  definite 
positions  of  equilibrium  among  important  components  of  a  solu- 
tion and  they  have  oriented  relations  hitherto  unsuspected.  But 
it  is  by  no  means  certain  that  we  have  attained  the  ultimate  con- 
ception of  what  our  measurements  represent  in  terms  of  mechan- 
isms. Better  descriptions  of  these  we  eagerly  await.  Scientific 
thought  pauses  where  it  is  convenient  and  leaps  forward  when 
necessity  demands;  but  experimental  measurements  remain  with 
whatever  force  skill,  scope  and  instrumental  precision  give  them — 
requiring  only  reinterpretation  with  the  enlargement  of  vision. 

In  a  crude  way  we  have  attempted  in  a  previous  chapter  to 
give  a  generalized  picture  of  oxidation-reduction  relations.  Here 
we  encounter  definite  experimental  facts  which  it  is  sometimes 
convenient  to  express  in  terms  of  "calculation  values."  It  may 
now  fairly  be  asked  whether  these  are  not  significant  as  indices 
of  equilibria  of  as  much  importance  to  the  delicate  adjustments 
of  life  processes  as  are  hydrogen  ion  concentrations.  If  the 
studies  so  far  made  are  prophetic  there  will  be  found  not  only 
a  profound  interrelationship  between  hydrogen  ion  concentrations 
and  oxidation-reduction  equilibria  but  also  direct  control  of  cer- 
tain biological  processes  by  the  reduction  potential  of  the  medium. 
See  Gillespie  (1920),  Clark  (1920)  and  Clark  and  Cohen  (1922) 


310  THE    DETERMINATION    OF   HYDROGEN    IONS 

for  some  applications  in  bacteriology.  See  also  -Chapters  XVI 
and  XX. 

Adsorption.  Hydrogen  and  hydroxyl  ions  are  particularly 
subject  to  adsorption  upon  surfaces.  Since  the  relative  activi- 
ties of  these  ions  are  especially  easy  to  measure,  methods  of  de- 
termining pH  are  of  great  value  for  adsorption  studies.  For  a 
review  of  recent  work  see  Michaelis  (1922). 

References.  Lachs-Michaelis  (1911),  Loffler-Spiro  (1919), 
Michaelis  (1922),  Michaelis-Rona  (1910,  1919,  1920),  Rona- 
Michaelis  (1919,  1920),  Tanner  (1922). 

Analyses.  The  empiricism  that  characterized  the  develop- 
ment of  analytical  methods  in  the  hands  of  Fresenius  and  others 
left  specifications  for  the  use  of  mixtures  of  acids,  such  as  acetic, 
and  their  alkaline  salts  in  many  separations.  These  we  now  know 
control  the  hydrogen  ion  concentration.  Here  and  there  in  the 
special  literature  are  to  be  found  the  calculated  hydrogen  ion  con- 
centrations in  such  cases  and  in  other  cases  directions  which  are 
somewhat  more  precise  than  the  customary  "slightly  acid"  or 
"slightly  alkaline."  More  recently  there  has  been  undertaken 
direct  experimentation  with  hydrogen  electrode  or  indicator  meth- 
ods. The  need  of  further  development  was  voiced  some  years  ago 
by  Dr.  Hillebrand  of  the  Bureau  of  Standards  when  he  indicated 
to  the  Washington  Chemical  Society  the  need  of  a  systematic  in- 
vestigation of  all  analytical  methods.  One  type  of  information 
urgently  needed  may  be  learned  from  the  papers  of  Blum,  of  Fales 
and  Ware  and  of  Hildebrand.  Colorimetric  pH  measurements  on 
carbonate  equilibria  are  furnishing  valuable  information  in  several 
simple  analytical  methods.  Kolthoff  is  working  on  the  relation  of 
pH  to  certain  oxidation-reduction  titrations.  Many  qualitative 
color  reactions  remain  to  be  studied. 

References.  Anger  (1921),  Behrend  (1893),  Bishop-Kittredge- 
Hildebrand  (1922),  Bogue  (1922),  Bottger  (1897),  Br0nsted  (1911), 
Blum  (1913,  1914,  1916),  Eastman-Hildebrand  (1914),  Fales- 
Ware  (1919),  Garard-Sherman  (1918),  Haas  (1916),  Hanzlik 
(1920),  Haskins-Osgood  (1920),  Hildebrand  (1913),  Hildebrand- 
Bowers  (1916),  Hildebrand-Harned  (1912),  Hopkins  (1921), 
Kober-Haw  (1916),  Kober-Sugiura  (1913),  Kolthoff  (1919-1921), 
Kolthoff-Volgelenzang  (1921),  Koritschoner-Morgenstern  (1919), 
Kramer-Green    (1921),    Kramer-Tisdale    (1921),   Liempt  (1920), 


APPLICATIONS  311 

Lizius  (1921),  Marriott  (1916),  Mattick- Williams  (1921),  Menten 
(1920),  Oettingen  (1900),  .  Osterhout  (1918),  Robinson 
(1919,  1922)  Robinson-Bahdemer  (1922),  Shohl  (1922), 
Sollmann  (1920),  Swanson-Tague  (1919),  Tague  (1920),  Till- 
mans-Bohrmann  (1921),  Tizard-Whiston   (1920),  Zoller  (1920). 

Autolysis  of  tissue  is  governed  by  the  activity  of  enzymes 
which  are  sensitive  to  the  concentration  of  hydrogen  ions.  As  the 
resultant  of  the  activity  of  two  types  of  enzymes  (Dernby)  auto- 
lysis is  controlled  by  the  pH  which  brings  into  play  the  activity  of 
each. 

References.  Bradley  (1916),  Bradley-Felsher  (1920),  Bradley- 
Taylor  (1916),  Dernby  (1917-1918),  Gibson-Umbreit-Bradley 
(1921),  Koehler-Severinghaus-Bradley  (1922),  Morse,  M.  (1916- 
1917). 

Bacteriology.  A  review  of  the  applications  in  bacteriology 
up  to  1917  is  given  by  Clark  and  Lubs  (1917). 

Adjustment  of  the  reaction  of  media  by  the  old  titrimetric  proce- 
dure was  criticised  by  Clark  (1915),  and,  on  the  introduction  of  suit- 
able indicators  and  the  evidence  for  the  advantage  of  adjusting 
on  the  pH  basis,  the  titrimetric  method  has  been  abandoned  for 
more  significant  and  easier  modern  methods.  Studies  on  growth 
optima  (which  see  below)  have  shown  that  for  the  cultivation  of 
most  saprophytes  approximate  indicator  control  without  the  use 
of  standards  is  sufficient  (see  Chapter  VIII) .  For  special  purposes 
and  especially  for  the  study  of  certain  important  pathogens  it  is 
well  to  adjust  with  the  precision  attained  with  standards.  Seldom 
is  electrometric  control  necessary. 

References.  Adam  (1921),  Baldwin  (1919),  Barthel  (1918-20), 
(1920),  Bovie  (1915),  Clark  (1915),  Clark-Lubs  (1916),  Conn 
(1919),  Cox-Wood  (1920),  Davis  (1920),  Dernby  (1919),  Fennei- 
Fisher  (1919),  Foster-Randall  (1921),  Graoe-Highberger  (1920), 
Henderson-Webster  (1907),  Hurwitz-Meyer-Ostenberg  (1915— 
1916),  Jones  (1919),  Kligler  (1917-1918),  Kligler-Defandorf  (1918), 
Ktister  (1921),  Mclntosh-Smart  (1920),  Massink  (1921),  Medical 
Research  Committee  (1919),  Michaelis  (1921),  Norton  (1919), 
Ponselle  (1920),  Reitstotter  (1920),  Stickdorn  (1922),  Wolf- 
Shunk  (1921). 

The  optimal  zones  and  the  limits  of  growth  and  general  metabolism 
have  naturally  been  the  chief  interest  in  the  first  surveys  of  the 


312  THE    DETERMINATION    OF   HYDROGEN   IONS 

influence  of  hydrogen  ion  concentration  upon  bacterial  activity. 
It  is  now  clear  that  in  the  future  more  exact  studies  will  have  to 
differentiate  between  optimal  initial  pH,  optimal  zones  of  growth, 
optimal  zones  for  general  or  special  metabolism,  optimal  zones 
for  preservation,  etc.  The  self  limitation  of  acid  fermentation, 
first  clearly  defined  by  Michaelis  and  Marcora  (1912),  has  been 
applied  to  certain  practical  tests;  for  example  see  Clark  (1915), 
Avery  and  Cullen  (1919).  pH  limits  for  special  organisms  which 
have  commercial  significance  are  exemplified  by  control  of  "rope" 
in  bread  (Cohn-Walbach-Henderson-Cathcart)  and  "scab"  on 
potatoes  (Gillespie-Hurst). 

References.  Adam  (1921),  Allen  (1919),  Avery-Cullen  (1919), 
Ayers  (1916),  Ayers-Johnson-Davis  (1918),  Barthel  (1918), 
Barthel-Sandberg  (1919),  Beckwith  (1920),  Bengtson  (1922), 
Boas  (1920),  Boas-Leberle  (1918),  Brown-Orcutt  (1920),  Bunker 
(1919),  Chambers  (1920),  Cheplin-Rettger  (1920),  Clark  (1915- 
18)  Clark-Lubs  (1915-1917),  Cohen-Clark  (1919),  Cohn-Wal- 
bach-Henderson-Cathcart  (1918),  Cole-Onslow  (1916),  Cole- 
Lloyd  (1917),  Colebrook  (1920),  Cullen-Chesney  (1918),  v.  Dam 
(1918),  Dernby,  (1921),  Dernby-Avery  (1918),  Dernby-Blanc 
(1921),  De  Kruif  (1922),  Duggar-Severy-Schmitz  (1917),  Erick- 
son-Albert  (1922),  Euler-Emberg  (1919),  Euler-Heintze  (1919), 
Evans  (1918),  Foster  (1920-1921),  Freear-Venn  (1920),  Fred- 
Davenport  (1918),  Frothingham  (1917-1918),  Gainey  (1918), 
Gates  (1919),  Gillespie  (1918),  Gillespie-Hurst  (1918),  Grace- 
Highberger  (1920),  Hagglund  (1915),  Hall-Fraser  (1921-1922), 
Henderson  (1918),  Holm-Sherman  (1921-1922),  Huddleson  (1921), 
Itano  (1916),  Itano-Neill  (1919),  Itano-Neill-Garvey  (1920), 
Johannessohn  (1912),  Johansen  (1920),  Jones  (1920),  Kiesel 
(1913),  Kligler  (1918),  Kligler-Robertson  (1922),  Kohman  (1919), 
Kniep  (1906),  Lazarus  (1908),  Levine  (1920),  Lord  (1919), 
Lord-Nye  (1919),  Lloyd  (1916),  Luers  (1914),  Meacham  (1918), 
Mellon  (1921),  Meyerhof  (1916-1917),  Michaelis-Marcora  (1912), 
Scheer  (1921),  Schoenholz-Meyer  (1919-1921),  Shaw-Mackenzie 
(1918),  Sherman  (1921),  Shohl-Janney  (1917),  Somogyi  (1921), 
Steinberg  (1919),  Svanberg  (1918-21),  Swartz  (1920)  Swartz- 
Shohl-Davis  (1921),  Waksman  (1918),  Waksman-Joffe  (1920- 
21),  Williams-Povitzky  (1921),  Winslow-Kligler-Rothberg  (1919) 
Wolf    (1918),    Wolf-Foster    (1921)    Wolf-Harris    (1917),    Wolf- 


APPLICATIONS  313 

Shunk  (1921),  Wolf-Telfer  (1917),  Wright  (1917),  Zeller-Schmitz 
(1919). 

The  influence  of  pH  upon  bacterial  metabolism.  The  reaction 
of  the  medium  even  within  the  zone  of  optimal  bacterial  growth 
is  found  to  influence  either  the  rate,  or  the  relative  rate  of  specific 
types  of  metabolism.  Not  only  the  activity  but  also  the  pro- 
duction of  enzymes  is  influenced  and  the  production  of  special 
products  such  as  toxins  is  partially  controlled  by  the  pH  of  the 
medium. 

References..  Arzberger-Peterson-Fred  (1920),  Avery-Cullen 
(1920),  Atkin  (1911),  Barthel  (1921),  Barthel-Bengtsson  (1920), 
Barthel-Sandberg  (1920),  Blanc-Pozerski  (1920),  Boas  (1919), 
Bronfenbrenner-Schlesinger  (1918),  Brooks  (1921),  Bunker  (1919), 
Charpentier  (1921),  Clark  (1920),  Cook-Mix-Culvyhouse  (1921), 
Davis  (1918,  1920),  Dernby-Aleander  (1921),  Dernby-Blanc 
(1921),  Dernby-David  (1921),  Euler-Blix  (1919),  Euler-Emberg 
(1919),  Euler-Hammarsten  (1916),  Euler-Svanberg  (1918,  1919), 
Fred-Peterson  (1920),  Gaarder-Hagem  (1920-1921),  Green  (1918), 
Groer  (1912)  Gustafson  (1920),  Itano  (1916),  Jacoby  (1918), 
Jones  (1920),  Lord-Nye  (1919),  Meyerhof  (1917),  Neuberg-Hirsch 
(1919),  Northrop-Ash-Senior  (1919),  Patty  (1921),  Peterson- 
Fred-Verhulst  (1921),  Robinson-Meader  (1920),  Sasaki  (1917), 
Stevens-Koser  (1920),  Venn  (1920),  Waksman-Joffe  (1921), 
Wolf  (1920),  Wyeth  (1919). 

Disinfectant  action  of  acids  and  bases  is  certainly  in  large  meas- 
ure a  function  of  hydrogen  or  hydroxyl  ion  concentration;  but 
specific  effects  of  certain  acids  and  bases,  which  were  suspected 
before,  have  now  been  more  clearly  demonstrated  by  the  use  of 
hydrogen  ion  methods.  With  the  conductivity  method  Winslow 
and  Lochridge  were  able  to  show  the  effect  of  the  hydrogen  ion 
in  simple  solutions  and  predicted  relations  which  more  powerful 
methods  have  extended  to  complex  media. 

Cohen  (1922)  has  reviewed  certain  relations  between  pH  and 
viability  of  bacteria  under  sub-lethal  conditions.  Time,  tempera- 
ture, and  pH  are  now  linked  as  controlling  factors  in  canning. 

The  more  direct  action  of  hydrogen  ion  concentration  upon 
cells  must  be  distinguished  from  its  control  upon  the  effective 
state  of  a  toxic  compound.  Knowledge  of  pH  effects  is  therefore 
essential  to  the  assay  of  disinfectants  and  to  the  advancement  of 
chemotherapy. 


314  THE    DETERMINATION    OF   HYDROGEN    IONS 

References.  Aubel  (1920),  Bettinger-Delaval  (1920),  Bial 
(1902),  Bigelow  (1921),  Bigelow-Cathcart  (1921),  Bigelow-Esty 
(1920),  Browning-Gulbransen  (1921),  Browning-Gulbransen- 
Kennaway  (1919),  Clark,  J.  F.  (1899),  Clark-Lubs  (1917),  Cohen 
(1922),  Cohen-Clark  (1919),  Donk  (1920),  Friedenthal  (1919), 
Kronig-Paul  (1897),  McClelland-Waas  (1922),  Mliller  (1921), 
Neilson-Meyer  (1921),  Norton-Hsu  (1916),  Paul-Birstein-Reuss 
(1910),  Paul-Kr6nig  (1896),  Rideal-Evans  (1921),  Shohl-Deming 
(1921),  Tawara  (1921),  .Traube-Somogyi  (1921),  Vermast  (1921), 
Waterman  (1915),  Weiss  (1921),  Winslow-Lochridge  (1906), 
Wolf-Foster    (1921),    Wright  (1917).     See  also  "Pharmacology." 

Acid  agglutination  of  bacteria,  first  definitely  recognized  by 
Michaelis  (1911)  in  its  relation  to  hydrogen  ion  concentration,  has 
been  found  to  be  of  some  diagnostic  use.  The  discovery  by  Ark- 
wright  of  separately  agglutinable  constituents  opened  up  some 
investigations  of  possibly  wide  bearing.  Buchanan  has  indicated 
some  of  the  possible  relations  to  serum  agglutination. 

References.  Arkwright  (1914),  Bach  (1920),  Barendrecht 
(1901),  Bechhold  (1904),  Beintker  (1912),  Beniasch  (1912), 
Bergey  (1912),  Bondorf  (1917),  Buchanan  (1919),  De  Kruif 
(1922),  Eisenberg  (1919),  (contains  review  and  bibliography), 
Field-Teague  (1907),  Georgi  (1919)  Gieszczykiewicz  (1916), 
Gillespie  (1914),  Grote  (1913-1914),  Heimann  (1913),  Jaffe" 
(1912),  Kemper  (1916),  Krumwiede-Pratt  (1913),  Tiess  (1919), 
Markl  (1915),  Michaelis  (1911,  1915,  1917),  Michaelis-Adler 
(1914),  Murray  (1918),  Poppe  (1912),  Radsma  (1919),  Schidor- 
sky-Reim  (1912),  Sears  (1913),  Sgalitzer  (1913),  Tulloch  (1914). 

d'Herelle  'phenomenon.     Gratia  (1921). 

Cell  interior.    Angerer  (1920). 

Testing  fermentation.  See  various  references  under  other  head- 
ings and  especially  Baker  (1922),  Chesney  (1922),  Clark  (1915- 
17),  Clark-Lubs  (1917),  Laybourn  (1920),  Nichols-Wood  (1922). 

Balloelectricity. 

Reference.     Christiansen-Christiansen  (1919). 

Beer.  As  originally  outlined  by  Pasteur  the  "reaction"  of 
wort  has  much  to  do  with  the  brewing  of  beer.  The  control  of 
"disease"  and  of  the  protein  material  held  in  solution  is  to  some 
extent  dependent  upon  pH  as  are  the  activities  of  the  enzymes 
concerned  at  each  stage. 


APPLICATIONS  315 

References.  Adler  (1915,  1916),  Emslander  (1914-1919), 
Leberle-Liiers>(1914),  Liiers(1914),Liiers-Adler  (1915),  Schjerning 
(1913).     See  also  "Bacteriology,"  "Enzymes"  and  "Proteins." 

Blood.  The  hydrogen  ion  concentration  of  the  blood,  while 
varying  slightly  among  normal  individuals,  is  regulated  with 
remarkable  constancy  in  any  one  individual  in  a  normal  environ- 
ment. It  never  varies  far  from  pH  7.4.  Van  Slyke  »(1921), 
places  the  normal  variation  between  about  7.3  and  7.5  and  the 
limits  compatible  with  life  at  approximately  7.0  and  7.8.  Since 
the  bicarbonate-carbonic  acid  equilibrium  is  one  of  the  most 
important  in  the  regulation  of  the  blood's  reaction  it  is  convenient 
to  define  the  system  in  terms  of  this  equilibrium.  See  "  carbonate 
equilibrium"  for  the  derivation  of  the  relation 

PH  =  pK1  +  log   [H^°J 


[free.  COd 


Inspection  of  the  relations  involving  the  carbonate  ion  CO 3 
(see  page  320)  will  show  that  at  pH  7.4  [CO3]  may  be  neglected 
and  the  fixed  carbon  dioxid  may  be  regarded  as  entirely  bicar- 
bonate. The  extent  of  the  bicarbonate  dissociation  is  in  doubt 
but  if  we  substitute  [BHCO3],  for  [HC03]  where  B  represents  any 
monovalent  base,  and  modify  pKi  to  accord  with  the  experimental 
conditions,  we  have 

pH  =  6.1  +  log  [BHC°3] 


[free  C02] 

[BHCO3J  -20 

The  ratio  - -p^r--,  determines   pH.     Normally  it  is   about— . 

[freeC02J  •  1 

From  one  point  of  view  the  blood  may  be  regarded  as  a  scav- 
enger, burning  the  waste  products  in  the  tissues  it  perfuses,  and 
carrying  off  the  final  products  of  combustion  of  which  C02  is  one 
of  the  most  important  for  the  acid-base  equilibria  under  con- 
sideration. With  a  given  content  of  buffer  in  the  blood  the 
hydrogen  ion  concentration  would  be  maintained  constant  under 
this  inflow  of  C02  by  the  maintenance  of  a  constant  C02  pressure 
in  the  lungs;  but  with  varying  buffer  content  the  hydrogen  ion 
concentration  could  only  be  maintained  constant  by  a  mechan- 
ism directly  responsive  to  hydrogen  ion  concentration  and  ca- 
pable of  altering  the  C02  pressure.     It  seems  that  the  respiratory 


316  THE    DETERMINATION    OF   HYDROGEN    IONS 

centre  is  thus  directly  responsive  to  the  hydrogen  ion  concentra- 
tion and  by  its  regulation  of  the  breathing  maintains  in  the 
alveolar  air  that  level  of  C02  pressure  which  is  in  harmony  with 
the  equilibria  centered  about  constant  pH  under  varying  condi- 
tions. Of  this  Haldane  says:  "The  respiratory  centre  is  enor- 
mously more  delicate  as  an  index  of  change  in  hydrogen  ion  con- 
centration of  the  blood  than  any  existing  physical  or  chemical 
method."  Clinical  methods  based  on  the  measurement  of  the 
alveolar  C02  tension  are  now  extensively  used  (see  Van  Slyke). 
On  the  other  hand,  the  C02  tension  is  but  one  item  of  a  compli- 
cated set  of  equilibria.  It  often  becomes  of  importance  to  know 
the  relative  proportions  of  the  other  constituents  of  the  acid- 
base  equilibria.  In  pathological  conditions  the  oxidative  proc- 
esses may  be  at  fault  and  the  carbonate  equilibria  must  be 
adjusted  to  accommodate  the  products  of  incomplete  combustion 
in  the  effort  of  the  body  to  maintain  constant  hydrogen  ion 
concentration  in  the  blood.  Therefore  it  becomes  important  to 
learn  the  relation  of  the  C02  content  to  the  alkaline  reserve. 
When  this  is  done  by  gas  chain  or  indicator  titrations  the  hydro-  / 
gen  electrode  and  indicator  methods  again  enter  the  subject 
from  which  they  were  to  some  extent  displaced  when  it  was  found 
that  there  was  no  particular  object  in  studying  a  constant  main- 
tained physiologically  with  a  degree  of  precision  often  beyond 
the  precision  of  experimental  measurement. 

Although  it  is  convenient  to  express  the  acid-base  equilibria 
of  the  blood  in  terms  of  the  bicarbonate  system  other  equilibria 
are  of  equal  importance  to  a  complete  description  of  the  mechan- 
isms. In  the  plasma  are  other  substances  beside  the  carbonic 
acid  and  bicarbonate  which  participate  in  the  acid-base  equilib- 
rium; but  the  most  interesting  relations  are  found  in  the  Donnan 
equilibrium  (see  page  328)  between  the  solutes  of  the  plasma  and 
the  material  trapped  within  the  membranes  of  the  blood  cells. 
Of  this  material  the  blood  pigment  is  the  most  important.  When 
oxidized  (as  oxyhemoglobin)  it  is  more  strongly  acidic  than 
when  reduced  (as  hemoglobin).  The  direct  consequence  is 
this:  when  the  blood  pigment  gives  up  oxygen  to  the  tissues  the 
blood  assumes  more  basic  properties  as  a  whole  and  is  thus  able 
to  take  up  more  C02  for  a  given  displacement  of  pH.  The 
converse  change  occurs  on  oxidation  in  the  lungs,  and  tends  to 


APPLICATIONS  317 

displace  CO2.     In  this  sense  the  blood  pigment  is  a  carrier  of  C02 
as  well  as  a  carrier  of  oxygen. 

Intimately  connected  with  the  regulation  of  the  hydrogen  ion 
concentration  of  the  blood  are  the  functions  of  the  kidneys  (see 
Cushny).  By  their  action  there  are  eliminated  the  non-volatile 
products  of  metabolism,  several  of  which  are  of  great  importance 
for  the  acid-base  equilibria  of  the  blood.  The  colorimetric  deter- 
mination of  the  pH  of  the  urine  is  a  comparatively  simple  pro- 
cedure which  furnishes  valuable  data  when  properly  connected 
with  other  data.  (See  for  instance  Blatherwick,  and  the  works 
of  Henderson,  of  Palmer  and  of  Van  Slyke.) 

While  the  greatest  interest  has  centered  in  the  subjects  briefly 
mentioned  above,  there  remain  innumerable  other  problems  of 
importance.  Of  these  there  may  be  mentioned  the  relation  of 
the  pH  of  the  blood  to  the  calcium-carrying  power,  to  the  activity 
of  various  enzymes,  to  the  permeabilities  of  tissue  membranes,  to 
the  activity  of  leucocytes,  and  to  various  reactions  used  in  the 
serum  diagnosis  of  disease. 

The  student,  if  bewildered  by  the  array  of  references  given 
below,  will  find  it  profitable  to  read  the  classic  work  of  Hender- 
son, Das  Gleichgewicht  zwischen  Basen  und  Sduren  im  tierischen 
Organismus.  By  following  the  papers  of  Van  Slyke  and  his  co- 
workers the  student  will  find  reviews  of  various  aspects  of  the 
subject.  The  respiration  phase  so  far  as  the  older  work  is  con- 
cerned will  be  found  in  Barcroft's  monograph.  The  later  work 
which  includes  the  effects  of  pH  is  reviewed  by  Bayliss,  Hender- 
son, Parsons  and  others.  Van  Slyke's  The  Carbon  Dioxide  Carriers 
of  the  Blood  (1921)  reviews  the  acid-base  equilibria  of  the  carbonate 
in  its  relation  to  the  acid-base  equilibria  of  the  hemoglobin,  phos- 
phate, etc. 

References  on  acid-base  equilibria  of  blood  and  related  mechanisms. 
See  also  "  Urine." 

1898 — Bugarszky-Tangl,  Spiro-Pemsel. 

1900— Hober. 

1901—  Rhorer. 

1902— Friedenthal,  Hober. 

1903 — Auerbach-Friedenthal,   Farkas,   Farkas-Scipiades, 
Fraenckel,  Friedenthal,  Hober,  Hober-Jankowsky. 

1904— Friedenthal. 


318  THE    DETERMINATION    OF   HYDROGEN   IONS 

1905—  Foa,  Pfaundler. 

1906—  Abel-Fiirth,  Benedict,  Szili. 
1907 — Aggazzotti. 

1908 — Henderson,  Henderson-Spiro,  Spiro-Henderson. 

1909 — Hendnrson,  Michaelis-Rona,  Ringer,  Robertson,  Szili. 

1910 — Hober,  Kreibich,  Robertson. 

1911 — Adler-Blake,  Bottazzi,  Hasselbalch-Lindhard,  Lob,  Po- 
lanyi,  Schwartz-Lemberger,  Skramlik,  Winterstein. 

1912 — Hasselbalch,  Hasselblach-Lundsgaard,  Lundsgaard,  Mi- 
chaelis-Davidoff,  Quagliariello-Agostino,  Quagliariello,  Roily, 
Salge,  Sellards. 

1913 — Elias-Kolb,  Henderson-Palmer,  Konikoff,  Masel,  New- 
burgh-Palmer-Henderson,  Palmer-Henderson,  Rona-Gyorgy, 
Rona-Takahashi,  Salge,  Snapper. 

1914 — Barcroft,  Blatherwick,  Michaelis,  Peabody,  Peters, 
Roily. 

1915 — Begun-Herrmann-Munzer,  Hasselbalch-Gammeltoft, 
Henderson-Palmer,  Levy-Rowntree-Marriott,  Ma.  de  Corral, 
Menten-Crile,  Milroy,  Momose,  Palmer-Henderson,  Poulton, 
Wilson-Stearns-Thurlow,  Winterstein. 

1916—  Gettler-Baker,  Haldane,  Hasselbalch-Lindhard,  How- 
land-Marriott,  Hurwitz-Lucas,  Levy-Rowntree,  Marriott,  Mc- 
Clendon,  McClendon-Magoon,  Macleod,  Reemlin-Isaacs, 
Rona-Ylppo,   Scott,    Ylppo. 

1917— Bienstock-Czaki,  Cullen,  Fitz-Van  Slyke,  Hasselbalch, 
Henderson,  Hober,  Hooker-Wilson-Connet,  Isaacs,  McClendon- 
Shedlov-Thomson,  Milroy,  Palmer-Van  Slyke,  Parsons,  Peters, 
Scott,  Stillman-Van  Slyke-Cullen-Fitz,  Van  Slyke,  Van  Slyke- 
Cullen,  Van  Slyke-Stillman-Cullen. 

1918— Bayliss,  Goto,  ■  Hasselbalch-Warburg,  Henderson- 
Haggard,  Macleod,  Macleod-Knapp,  Sonne-Jarlov,  Straub- 
Meier,  Zunz. 

1919— Debenham-Poulton,  Donegan-Parsons,  Haggard-Hender- 
son, Haskins,  Irwin,  Macleod,  Parsons,  Schloss-Harrington,  Van 
Slyke-Stillman-Cullen,  Van  Slyke-Austin-Cullen. 

1920— Anon,  Bayliss,  Bisgaard-N0rvig,  Blatherwick,  Campbell- 
Poulton,  Collip,  Collip-Backus,  Coulter,  Dale-Evans,  Davies-Hal- 
dane-Kennaway,  Dragstedt,  Forbes-Halverson-Schulz,  Fredericia, 
Grant,  Goldman,  Parsons,  Haggard-Henderson,  Hartridge,  Haskins- 


APPLICATIONS  319 

Osgood,  Henderson,  L.,  Henderson,  Y.,  Henderson-Haggard- 
Coburn,  Hills,  Joffe-Poulton,  v.  Kapff,  MacNider,  Mellanby- 
Thomas,  Menten,  Michaelis,  Moore,  Parsons,  Parsons-Parsons, 
Parsons-Parsons-Barcroft,  Parsons-Shearer,  Prentice-Lund-Harbo, 
Priestley,  Raymund,  Reimann,  Rieger,  Suitsu,  Van  Slyke- 
Palmer. 

1921 — Barr-Peters,  Bazett-Haldane,  Busa,  Chistoni,  Collip, 
Doisy-Eaton,  Evans,  C.  L.,  Fleisch,  Gauss,  Haggard-Henderson, 
Haldane,  Hastings-Murray-Murray,  Henderson,  Hill,  Jarloev, 
Ma.  de  Corral,  Means-Bock- Woodwell,  Meier-Kronig,  Parsons- 
Parsons,  Peters-Barr,  Peters-Barr-Rule,  Reimann-Reimann, 
Reimann-Sauter,  Roaf,  Smith-Means-Woodwell,  Trevan-Boock, 
Van  Slyke,  Van  Slyke-Stadie,  Winterstein. 

1922 — Barach-Means-Woodwell,  Barkan-Broemser-Hahn,  Cul- 
len,  Coulter,  Doisy-Briggs-Chouke,  Henderson,  Hirsch-Peters, 
Hirsch- Williams,  Macleod,  Parsons-Parsons,  Williams-Swett. 

Bread.  In  the  baking  of  bread  it  is  essential  that  the  proteins, 
such  as  glutin,  which  are  responsible  for  the  holding  of  the  gas, 
shall  be  conditioned  by  the  proper  pH.  The  pH  may  also  control 
the  growth  of  the  "rope"  organism.  The  activity  of  yeast  and 
the  evolution  of  CO2  from  baking  powders  have  relations  to  the 
pH  of  the  dough. 

References.  Bailey-Peterson  (1921),  Cohn-Cathcart-Hender- 
son  (1918),  Cohn-Henderson  (1918),  Cohn-Walbach-Henderson- 
Cathcart  (1918),  Freear-Venn  (1920)  Henderson  (1918),  Hen- 
derson-Cohn-Cathcart-Wachman-Fenn  (1919),  Henderson-Fenn- 
Cohn  (1919),  Jessen-Hansen  (1911),  Landenberger-Morse  (1918) 
(1919),  Liiers  (1920),  Patten  (1920),  Sharp-Gartner  (1922),  Wahl 
(1916). 

Breeding.  Control  of  spermatozoan  activity.  See  "Compara- 
tive and  General  Physiology,"  and  C.  G.  L.  Wolf  (1921). 

Body  Fluids  (other  than  blood,  urine,  digestive  juices,  cere- 
brospinal fluid). 

References.  Aggazzotti  (1921),  Bloomfield-Huck  (1920),  Collip 
(1920),  Farkas-Scipjades  (1903),  Foa,  (1905,  1906),  Fraenckel 
(1905),  Gies  (1916),  Goldberger  (1917),  Hertel  (1921),  Huddelson 
(1921),  Lob-Higuchi  (1910),  Loeb-Atchley-Palmer  (1922),  Long- 
Fenger  (1915,  1916),  Marshall  (1915),  Michaelis-Kramsztyk 
(1914),  Okada  (1915),  Quagliariello  (1916-1921),  Schade-Neu^ 
kirch-Halpert   (1922),   Shepard-Gies   (1916),  Uyeno   (1919). 


320 


THE  DETERMINATION  OF  HYDROGEN  IONS 


Canning.  The  National  Canners'  Laboratory  has  so  related 
time,  temperature  and  pH  that  economy  and  certainty  in  the 
commercial  sterilization  of  canned  foods  can  be  assured. 

References.  Bigelow  (1921),  Bigelow-Cathcart  (1922),  Koh- 
man  (1922),     Rogers-Deysher-Evans  (1921). 

Carbonate  Equilibria.  When  carbon  dioxid  dissolves  in 
water  without  any  base  to  form  carbonate  there  are  presumably 
present  in  the  water  both  anhydrous  C02  and  the  hydrate, 
H2CO3,  carbonic  acid.  Analytical  methods  do  not  ordinarily  dis- 
tinguish these  two  forms,  and,  since  the  sum  of  the  two  is  generally 
the  more  important  quantity,  we  may  write  the  equilibrium  equa- 
tion for  the  relation  between  a  partial  pressure,  P,  of  gaseous 
carbon  dioxid  and  the  dissolved  carbon  dioxid  as  follows: 

[C02]  +  [H2C03]  =  [free  C02]  =  KoP 

In  the  presence  of  bases  we  still  have  the  above  relation  holding 
tbetween  the  partial  pressure  and  that  portion  of  the  total  CO2 
c which  remains  uncombined.  However,  variation  in  the  composi- 
tion of  the  solution  will  vary  the  magnitude  of  K0.  We  probably 
make  no  significant  error  if  we  regard  [free  C02]  in  carbonate  solu- 
tions to  be  influenced  by  the  total  salt  (carbonate)  just  as  it  is 
influenced  by  the  total  salt  concentration  in  a  solution  containing 
no  base.  On  this  basis  Johnston  (1915)  uses  Bohr's  data  for 
the  absorption  coefficients  of  carbon  dioxid  in  sodium  chlorid 
solutions  of  different  concentration,  and  calculates  therefrom 
the  values  of  Kq  in  terms  of  molar  concentration. 

Johnston's  table  of  K0 


TEMPERATURE 

IN  WATER 

IN  1 . 17  M  SALT 

IN  3.44M  SALT 

3.5 

0.0672 

0.0484 

0.0270 

4.2 

0.0500 

0.0367 

0.0213 

16.0 

0.0441 

0.0328 

0.0193 

25.0 

0.0338 

0.0260 

0.0159 

30.0 

0.0297 

0.0232 

0.0142 

40.0 

0.0236 

0.0185 

0.0117 

From  these  values  Johnston  interpolates  the  following  values 
of  K0  for  the  indicated  concentrations  of  total  base  or  salt  at 

1 


25°C.     Included    below    are    the    values    of    pKo    =    log 


Ko' 


APPLICATIONS 


321 


TOTAL  BASE 
OR  SALT 

0.0 

0.1 

0.2 

0.3 

0.5 

1.0 

K0 

pK„ 

0.0338 
1.471 

0.0329 
1.483 

0.0321 
1.493 

0.0314 
1.503 

0.0300 
1.523 

0.0270 
1.569 

Dissolved  C02  reacts  with  water  and  since  [H2O]  may  be  regarded 
as  constant  we  have  the  equilibrium  equation 


[CQ 


[H2CO; 


=  K,Qr  [CQ2l  +  [HsCOa]  =  K,+  x 


[H2C03 


(68) 


The  H2C03  dissociates  in  steps  and  for  the  first  step  the  equilib- 
rium condition  is 


[H+]  [HCQ3] 
[H2C03] 


=  K" 


69) 


Combining  equations  (68)  and  (69)  and  collecting  constants  we 
have 

[H+]  [HCO3]     = 
[COJ  +  [H2C03] 

or  using  the  convention  mentioned  above 
[H+]  [HCO3] 


[free  C02] 


=  Ki 


(70) 


The  constant  Ki  is  sometimes  called  the  first  dissociation  con- 
stant of  carbonic  acid.  It  is  not  strictly  so  but  is  rather  of  the 
nature  of  an  "apparent  dissociation  constant."  Ki  is  more  use- 
ful than  the  true  dissociation  constant  but  is  probably  much 
smaller. 

For  the  second  stage  of  dissociation  the  equilibrium  condition  is: 


[H+]  [CO,] 


=  K2 


(71) 


[HCO3] 

In  addition  to  these  equations  there  is  the  useful  relation 
)f  electrical  neutrality, 

[B+]  +  [H+]  =  [HCOj  +  2  [C03]  +  [OH]  (72) 

vhere  [B+]  represents  the  total  concentration  of  cations  other  than 
H+]  and  all  species  are  represented  in  equivalent  concentrations. 


322  THE    DETERMINATION    OF   HYDROGEN    IONS 

One  of  the  chief  experimental  difficulties  in  handling  carbonate 
solutions  is  the  control  or  the  evaluation  of  P.  But  while  this 
is  susceptible  to  management  the  correct  evaluation  of  Ki  and 
K2  is  a  matter  of  great  complexity  for  the  following  reasons.  If 
salts  such  as  Na2C03  and  NaHC03  are  used  as  experimental  ma- 
terial to  establish  various  proportions  of  carbonate  and  bicarbon- 
ate ions  it  becomes  necessary  to  know  the  degree  of  their  dis- 
sociation at  known  concentrations  of  the  salts,  or  if  complete 
dissociation  occurs  it  becomes  necessary  to  know  the  effect  of 
different  concentrations  upon  activities.  This  involves  the  whole 
unsettled  question  of  the  conduct  of  "strong  electrolytes."  Hith- 
erto there  have  been  carried  over  to  pH  studies  the  constants 
derived  by  the  use  of  conductivity  data  which  are  not  strictly 
applicable. 

If  yi  represents  the  degree  of  dissociation  of  NaHCC>3  and 
y2  degree  of  dissociation  of  Na2C03  we  have  the  following  rela- 
tions according  to  Seyler  and  Lloyd  (1917). 

[Na] 0.05      0.1         0.2         0.3         0.5         1.0 

y! 0.82      0.78        0.73        0.69        0.64        0.52 

y2 0.56      0.66        0.37        0.31        0.24        0.14 

Space  does  not  permit  a  detailed  discussion  of  the  above  values 
and  numerous  other  quantities  which  enter  into  the  data  of 
carbonate  equilibria.  We  shall  proceed  with  the  more  general 
relations  indicated  by  the  pure  equilibrium  equations  and  shall 
give  without  comment  Johnston's  values  for  the  more  important 
constants. 

Putting  the  equations  into  logarithmic  form,  and  using  for 

terms  such  as  log  ^  the  expression  pK,  we  have  the  following 
useful  relations: 

pH  =  pKi  +  log  [HC03]  -  log  [free  C02]  (73) 

pH  =  pKi  +  pK0  +  log  [HCO3]  -  log  P  (74) 

pH  =  pK2  +  log  [C03]  -  log  [HCO3]  (75) 

pH  =  I  pK0  +  \  pKx  +  \  pK2  -  \  log  P  +  \  log  [C03]    (76) 

m+1  J  2X0^1^  +  KpKxP  [H+]  +  Kw  [H+]  -  [H+P 

L     J  [H+]2    , 

For  the  values  of  pK0  see  page  320.    From  Johnston's  selected 


APPLICATIONS 


323 


values  for  the  first  and  second  acid  dissociation  constants  at 
25°C.  we  have  pKi  =  6.47  and  pK2  =  10;32.  For  other  values 
see  references. 

Inspection  of  the  combined  equations  will  show  that  pH  is 
denned  by  any  two  of  the  variables  or  conversely  that  pH  and 
one  variable  determine  the  state  of  a  carbonate  equilibrium. 
By  the  use  of  equation  (77)  the  total  base  can  be  brought  into 
consideration  and  it  can  be  shown  that  the  total  base  and  one 
variable  such  as  pH  or  P  will  define  the  position  of  a  carbonate 
equilibrium.  See  (77).  Thus  a  carbonate  solution  exposed  to  the 
atmosphere  with  its  more  or  less  constant  partial  pressure  of 
C02  at  0.0003  atmosphere  will  tend  to  reach  a  definite  pH  value 
which  is  determined  by  the  total  base.  This  may  be  as  low  as 
pH  5.0  for  solutions  containing  very  little  base  or  as  high  as  pH 
10  in  a  solution  about  normal  with  respect  to  [B+].  Based  upon 
such  relations  are  analytical  methods  for  determining  C02  par- 
tial pressures  from  pH  and  known  concentrations  of  total  base. 

Equations  (73)  and  (74)  are  of  importance  in  the  study  of  blood 
the  pH  of  which  may  be  defined  in  terms  of  the  ratio  of  bicarbonate 
to  free  C02  or  in  terms  of  bicarbonate  and  P.  See  section  on 
blood.  Direct  experimental  data  for  which  equation  (75)  ex- 
presses the  fundamental  relations  are  given  as  follows  by  Auer- 
bach  and  Pick  (1912): 


pH  values  for  mixtures  of  sodium  carbonate  and  bicarbonate   at  18  C.  after 
Auerbach  and  Pick 


MOLS  PES  LITRE 

MOLS  PER  LITHE 

pH 

pH 

'  NaHCOa 

NasCOi 

NaHCOs 

Na2C03 

0.20 

0.00 

8.35 

0.10 

0.000 

8.35 

0.19 

0.01 

8.90 

0.09 

0.005 

8.98 

0.18 

0.02 

9.15 

0.08 

0.010 

9.30 

0.16 

0.04 

9.45 

0.07 

0.015 

9.50 

0.14 

0.06  • 

9.65 

0.06 

0.020 

9.60 

0.12 

0.08 

9.96 

0.05 

0.025 

9.87 

0.10 

0.10 

10.10 

0.04 

0.030 

10.05 

0.08 

0.12 

10.35 

0.03 

0.035 

10.23 

0.06 

0.14 

10.45 

0.02 

0.040 

10.35 

0.04 

0.16 

10.65 

0.01 

0.045 

10.7 

0.02 

0.18 

11.0-11.8 

0.00 

0.050 

11.4 

0.00 

0.20 

11.59 

324  THE    DETERMINATION    OF   HYDROGEN   IONS 

Equation  (76)  is  of  importance  when  it  is  desired  to  know 
the  relations  between-  partial  pressure  of  C02  and  the  state  of 
some  carbonate  equilibrium  such  as  that  of  calcium  carbonate. 
In  this  case  we  have  another  set  of  relations.  Calcium  carbonate 
is   but  slightly  soluble    per    se.     In   the    equilibrium    equation 

[Ca++]  [CO,]  =  K 
[CaC03] 

we  often  have  to  deal  with  a  constant  value  of  CaC03  maintained 
by  the  presence  of  solid  CaC03.  Under  such  circumstances  we 
may  combine  this  constant  with  the  dissociation  constant  giving 

[Ca++]  [C03]    =    K8  (78) 

where  K8  is  the  "solubility  product." 

By  combining  (78)  with  (76)  it  is  seen  how  Ca++  can  be  gov- 
erned by  P,  a  relation  of  geological  importance. 

K8  varies  with  the  nature  of  the  solid  phase,  (Calcite,  Aragonite 
or  precipitated  calcium  carbonate  of  different  states  of  fineness). 
It  is  of  the  order  of  1  X  10-s. 

The  equations  of  carbonate  equilibria  have  been  left  in  their 
more  general  form  to  show  the  more  general  relations.  Modi- 
fications for  special  purposes  are  very  numerous  and  beyond 
the  scope  of  this  sketch.  For  detailed  treatment  see  references 
under  "Analyses,"  "Blood,"  "Water,"  "Equilibria,"  etc.  A 
treatment  of  the  general  biological  importance  of  the  carbonate 
equilibria  is  given  in  The  Fitness  of  the  Environment  by  Henderson. 

References.  Auerbach-Pick  (1912),  Bjerrum-Gjaldbaek  (1919), 
Frary-Nietz  (1915),  Henderson  (1913),  Henderson-Black  (1908), 
Johnston  (1915,  1916),  Johnston-Williamson  (1916),  McClendon 
(1917),  McClendon-Shedlov-Thomson  (1917),  Michaelis-Rona 
(1914),  Prideaux  (1915),  Seyler-Lloyd  (1917),  Thiel-Stroheker 
(1914),  Tillmans  (1921),  Van  Slyke  (1917,  1922),  Wagner-Enslow 
(1922),  Walker-Cormack  (1900),  Wilke  (1921)-,  Windish-Dietrich 
(1920). 

Catalysis.  The  catalytic  activity  of  the  hydrogen  and  the 
hydroxyl  ions  in  such  transformations  as  the  hydrolysis  of  cane 
sugar  has  taken  a  prominent  place  in  the  development  of  the  theory 
of  electrolytic  dissociation.     Under  limited  conditions  one  or  an- 


APPLICATIONS  325 

other  of  these  catalytic  processes  is  proportional  to  the  concentra- 
tion of  the  hydrogen  or  the  hydroxyl  ions;  but  there  may  enter 
the  action  of  neutral  salts.  The  theory  of  their  influence  is  now 
being  recast  in  accord  with  the  concept  of  "activity."  The  older 
literature  on  hydrogen  and  hydroxyl  ion  catalyses  is  reviewed 
in  the  monograph  by  Woker  (1910,  1915).  A  few  recent  refer- 
ences are:  Abel  (1920),  Akerlof  (1921),  Jones-Lewis  (1920),  Kailan 
(1920),  Karlson  (1921),  Northrop  (1921).  See  Enzymes,  Salt 
Action  and  Chapter  XX. 

Cerebrospinal  Fluid. 

References.  Bisgaard  (1913),  Botazzi-Craifaleanu  (1916),  Col- 
lip  (1920),  Felton-Hussey-Bayne-Jones  (1917),  Hertel  (1921), 
Hurwitz-Tranter  (1916),  Levinson  (1917,  1919),  Meier  (1921), 
Shearer-Parsons  (1921),  Weston  (1916). 

Cheese. 

References.  AUemann  (1912),  Barthel-Sandberg  (1919),  Okuda- 
Zoller  (1921),  van  Dam  (1910). 

Colloids.  That  the  dispersion  of  colloids  may  be  influenced 
by  the  "reaction"  of  the  medium  has  long  been  known.  So  widely 
scattered  is  the  literature  on  this  particular  phase  of  colloid  chem- 
istry that  the  author  has  made  no  attempt  to  assemble  it.  It 
is  through  the  study  of  protein  solutions  that  the  most  distinctive 
advances  have  been  made.  Beginning  with  Hardy  the  study 
of  proteins  as  amphoteric  electrolytes  has  been  carried  forward 
by  Pauli,  Michaelis,  Robertson,  S0rensen,  Henderson,  Loeb  and 
others  until  there  has  developed  a  distinct  protest  against  the 
separation  of  certain  of  the  phenomena  of  colloids  from  the  appli- 
cation of  the  simpler  relations  of  crystalloids.  How  far  the  matter 
nay  be  pushed  in  its  application  to  other  types  of  material  taking 
he  "colloidal  state"  remains  to  be  determined. 

A  very  good  discussion  of  the  relation  of  the  developments  in 
>rotein  chemistry  to  colloid  chemistry  is  given  by  S0rensen  (1917). 
Compare  Loeb,  1922.) 

References.  Abderhalden-Fodor  (1920),  Adolf -Pauli  (1921), 
Arrhenius  (1922),  Bethe  (1920),  Clowes  (1913),  Ellis  (1911) 
:,abes  (1921),  Lachs-Michaelis  (1911),  Lillie  (1909),  McBain- 
!  almon  (1920),  McDougal-Spoehr  (1919),  McGuire-Falk  (1922), 
:  leier-Kronig  (1921),  Michaelis  (1920,  1921,  1922),  Michaelis- 
:tona  (1919-1920),  Ostwald  (1912),  Perrin  (1904),  Procter  (1921), 


326  THE    DETERMINATION    OF   HYDROGEN    IONS 

Rona-Michaelis  (1919),  Schoucroum  (1920),  Smith  (1920), 
Spiro  (1916),  Stiegler  (1921),  Varga  (1919),  Walpole  (1914) /Will- 
iams (1920).  See  also  "Proteins,"  "Adsorption,"  "Donnan 
Equilibrium,"  "  Electrophoresis." 

Comparative    and  General  Physiology. 

References.  Aggazzotti  (1913),  Andrus  (1919),  Arrhenius  (1921), 
Atkins  (1922),  Barkan-Broemser-Hahn  (1922),  Barratt  (1905), 
Bernstein  (1913),  Bethe  (1909),  Brenner  (1921),  Broderick  (1921), 
Burgh-Clark  (1921),  Burridge  (1920,  21),  Carr  (1921),  Clowes- 
Smith  (1922),  Cohn  (1917),  CoUett  (1919,  1921),  Collip  (1920- 
1921),  Coulter  (1920),  Cremer  (1906),  Crozier  (1915-19),  Dale 
(1913),  Dale-Thacker  (1914),  Fletcher-Hopkins  (1907),  Galeotti 
(1906,  1920),  Garrey  (1920),  Girard  (1909),  Goldberger  (1917)/ 
Gray  (1920),  Hampshire  (1921),  E.  N.  Harvey  (1920),  R.  B. 
Harvey  (1920),  Hastings-Murray  (1921),  Herbst  (1904),  Hirsch 
(1921),  Hiruma  (1917),  Hober  (1910),  Hopkins  (1921),  Hurwitz 
(1910),  Ivy-Oyama  (1921),  Jacobs  (1920-22),  Jameson-Atkins 
(1921),  Jewell  (1920),  Kahlenberg  (1900),  Kastle  (1898),  Kopac- 
zewski  (1914),  Kfizencky  (1916),  Langefeldt  (1921),  J.  Loeb, 
(1898,  1903,  1904,  1906),  Loeb-Wasteneys  (1911),  R.  Loeb  (1920), 
Lloyd  (1916),  MacArthur  (1920),  McClendon  (1916,  1920), 
McClendon-Mitchell  (1912),  MacDougall  (1921),  Meyerhof  (1918), 
Mines  (1912),  Moore  (1919,  1920),  Moore-Roaf- Whitley 
(1905),  Moore-Whitley-Webster  (1921),  Morse-Goldberg 
(1922),  Neilson-Meyer  (1921),  Neugarten  (1919),  Oden  (1916), 
Ostwald-Kuhn  (1921),  Parnas-Wagner  (1914),  Pechstein 
(1915),  Philippson-Hannevart  (1920),  Plotho  (1920),  Popielski 
(1919),  Porcelli-Titone  (1914),  Powers  (1921-22),  Prentice- 
Lund-Harbo  (1920),  Reichel  (1922),  Resch  (1917),  Richards 
(1898),  Ritchie  (1922),  Roaf  (1912-1922),  Rohde  (1920),  Rona- 
Wilenko  (1914),  Roncati-Quagliariello  (1921),  Roth  (1917), 
Saunders  (1920),  Schwyzer  (1914),  Shelford-Powers  (1915), 
Shohl  (1914),  Straub-Meier  (1919),  Traube  (1920),  Warburg 
(1910),  Wells  (1915),  Whitley  (1905),  Wolf  (1921). 

Crystallography.  Wherry  (private  communication)  states 
that  there  is  reason  to  believe  that  the  pH  of  a  medium  may  some- 
times control  crystal  form. 

Culture  of  organisms  other  than  bacteria,  plants  and  tissue. 

References.     Bodine,  (1921),  Young-VanSant  (1922).     See  also 


APPLICATIONS  327 

numerous  notes  in  references  under  "Comparative  and  General 
Physiology,"   "Bacteriology,"  and  "Tissue  culture." 

Dakin's  Solution. 

Reference.     Cullen- Austin  (1918). 

Digestive  System.  The  digestive  tract  is  primarily  the  chan- 
nel for  the  intense  activity  of  hydrolytic  enzymes  and  as  such  is 
provided  with  mechanisms  for  the  establishment  of  hydrogen  ion 
concentrations  favorable  to  these  enzymes.  Hydrogen  electrode 
methods  have  correlated  the  regional  activity  of  particular  en- 
zymes with  the  reactions  there  found,  have  clarified  some  of  the 
differences  between  the  digestive  processes  of  infancy  and  adult 
life,  aided  in  the  explanation  of  the  acid  and  alkali  formation,  and 
have  been  of  service  in  the  improvement  of  clinical  methods  for  the 
assay  of  pepsin  activity  and  the  diagnosis  of  abnormal  secretion 
of  hydrochloric  acid  in  the  stomach.  The  control  of  specific  phys- 
iological functions  such  as  secretion  of  conditioning  agents  (see 
Bayliss,  1918),  permeabilities,  and  activities  of  the  varied  muscu- 
lature, as  well  as  investigations  upon  the  condition  in  the  digestive 
tract  of  substances  such  as  calcium  and  phosphate  which  form  in- 
soluble precipitates  are  subjects  which  present  promising  material 
for  the  application  of  modern  methods.  Shohl  and  King  (1920) 
have  recently  reviewed  and  improved  methods  of  studying 'gas- 
tric acidity. 

References.  Allaria  (1908),  Ambard-Foa  (1905),  Auerbach- 
Pick  (1912,  1913),  Cannon  (1907),  Christiansen  (1911,  1912, 
1921),  Davidsohn  (1911, 1912, 1913, 1921),  Foa  (1905,  1906),  Fow- 
ler-Bergeim-Hawk  (1915),  Fraenckee  (1905),  Graham  (1911), 
Hahn  (1914),  Hainiss  (1921),  Hammett  (1922),  Hess  (1915), 
Hess-Scheer  (1921),  Howe-Hawk  (1912),  Huenekens  (1914), 
Krummacher  (1914),  Lanz  (1921),  Long-Fenger  (1917),McClendon 
(1915,  1920),  McClendon-Bissell-Lowe-Meyer  (1920),  McClen- 
don  Myers-Culligan-Gydesen  (1919),  McClendon-Shedlov-Thom- 
son  (1917),  McClendon-Shedlov-Karpman  (1918),  McWhorter 
(1918),  Menten  (1915),  Michaelis  (1917,  1918,  1920),  Michaelis- 
Davidsohn  (1910),  Myers-McClendon  (1920),  Nelson-Williams 
(1916),  Okada-Arai  (1922),  Popielski  (1919),  Rolph  (1915), 
Rona-Neukirch  (1912),  Salge  (1912),  Scheer  (1921),  Schryver- 
3inger  (1913),  Shohl  (1920),  Shohl-King  (1920),  Tangl  (1906), 
IYaube  (1920),  Ylppo  (1916). 


328 


THE  DETERMINATION  OF  HYDROGEN  IONS 


Dissociation  Constants  as  determined  with  the  hydrogen 
electrode  or  indicator  methods.     Compare  Chapter  I. 

References.  Agostino-Quagliariello  (1912),  Dernby  (1916), 
Eckweiler-Noyes-Falk  (1920),  Eijdman  (1906),  Kastle  (1905), 
Kolthoff  (1918,  1920),  Michaelis  (1911,  1913,  1914),  Michaelis- 
Garbendia  (1914),  Michaelis-Rona  (1913,  1914,  Prideaux  (1911), 
Salm  (1906,  1908),  Scudder  (1914),  Tizard  (1910),  Weisse-Meyer 
Levy  (1916).     See  Indicator  constants. 

Donnan  Equilibrium.  Imagine  a  solution  of  a  simple  elec- 
trolyte and  a  membrane  permeable  to  the  electrolyte.  Upon 
one  side  of  the  membrane  let  there  be  a  solution  of  a  substance 
which  cannot  penetrate  the  membrane  but  which  can  enter  into 
the  equilibrium  of  the  simple  electrolyte.  A  simple  case  is  the 
following.  Let  the  initial  state  be  illustrated  by  the  following 
scheme  where  there  is  placed  upon  one  side  of  the  membrane 
M  a  dilute  solution  of  HC1  and  upon  the  other  side  the  acid  HR 
neither  the  anion  nor  the  undissociated  residue  of  which  can 
penetrate  the  membrane. 


[HR], 


M 


[HC1]2 

[H+]2 

[CI]. 


Chlorine  ions  (or  HC1)  will  diffuse  from  right  to  left  until, 
when  equilibrium  is  attained,  there  will  be  the  following  state 


[HC1]3 

[HR], 

[H+]3 

[R]3 

[CI]. 


M 


[HC1], 

[H+]4 

[CI], 


If  now  we  place  hydrogen  electrodes  on  the  two  sides  of  the 
membrane  the  E.  M.  F.  of  this  gas  chain  will  be  determined  in 
part  by  the  relative  concentrations  of  the  hydrogen  ions  and  in 
part  by  a  potential  difference  across  the  membrane.  This  mem- 
brane potential  difference  we  shall  call  Ed 


E.M.F.  =  5Tln|5!I3 
nF       [H+]4 


+  Ed 


We  may  also  place  on  the  two  sides  electrodes,  the  potential 
differences  at  which  are  determined  by  the  relative  concentrations 


APPLICATIONS  329 

of  the  chlorine  ions  (e.  g.  Pt-Cl  electrodes  or  calomel  electrodes). 
For  such  a  chain  we  would  have 

E.M.F.  =  —  ln[2|4  +  Ed 
nF       [Cl]3 

We  have  already  specified  however  that  the  system  is  at  equilib- 
rium. Therefore  no  energy  could  be  obtained  from  either  one 
of  the  chains  described  above.  The  E.  M.  F.  in  each  case  is 
then  zero  and  since  Ed  is  the  same  in  each  case 

[H+]»  =  [Oj* 

[H+]4     [a]. 

The  rule  of  electrical  neutrality  indicates  that  on  the  right  side 
of  the  membrane  [H+]4  =  [Cl_]4.  Combining  this  relation  with 
the  other  we  then  have 

[H+]42  =  [H+]3  [Cl]3 

There  are  various  directions  in  which  we  may  now  proceed. 
As  one  example  let  us  assume  the  very  simple  case  where  the 
dissociations  of  HR  and  HC1  are  complete,  and  let  us  further 
assume  that  the  system  is  divided  by  the  membrane  into  two 
equal  parts.  Between  the  initial  and  the  final  state  of  the  sys- 
tem chlorine  ions  have  diffused  from  right  to  left  until  the  con- 
centration [Cl]3  is  x.  Then  [H+]3  =  [H+]x  +  x  and  [H+]4=  [H+]s 
—  x.  Introducing  these  values  into  the  foregoing  equation  we 
have 

([H+]2  -  x)2  =  x  ([H+],  +  x) 


>r 


[H+]2  -  x  _  [H+]2  +  [H+]i  or  x  =  [H+tf 


x  [H+]2  [H+li  +  2[H+]2 

The  following  table  will  give  an  idea  of  the  magnitude  of  the 
effects  due  to  the  conditions  assumed. 

As  we  have  already  indicated,    the  difference  of  potential  be- 

ween  two  hydrogen  electrodes  placed  on  opposite  sides  of   the 

)  aembrane  must,  at  the  equilibrium  state  of  the  system,  be  equal 

;  nd  opposite  to  the  potential  difference  at  the  membrane.    Hence 


330 


THE  DETERMINATION  OF  HYDROGEN  IONS 


the  membrane  potential  difference  may  be  expressed  in  terms  of 
a  hydrogen  electrode  gas  chain: 

RTln[H+]3 
F        [H+]/ 

By  using  this  relation  we  calculate  the  membrane  potential 
difference  given  in  millivolts  in  the  last  column  of  the  following 
table. 


[Ri»-[H+], 

[H+], 

INITIAL  KATIO 

[H+J. 

[H+], 

PER  CENT  HC1 
DIFFUSED  TO 

ESTABLISH 
EQUILIBRIUM 

EQUILIBRIUM 
DISTRIBUTION 

[H+], 

RATIO  z xr 

[H+]4 

MEMBRANE 

POTENTIAL  IN 

MILLIVOLTS 

0.01 

1.0 

1.0 

1.0 
1.0 
0.01 

0.01 
1.0 
100.0 

49.8 
33.3 
0.98 

1.01 
2.0 
101.0 

-  0.3 

-  18.0 
-120.0 

Of  course  the  conditions  assumed  for  purposes  of  illustration 
are  extremely  simple  but  they  suffice  to  indicate  the  nature  of 
relations  of  very  great  importance  in  the  physiology  of  the  living 
cell. 

References.  Donnan  (1911),  Donnan-Harris  (1911),  Loeb 
(1921-22),  Michaelis  (1922),  Moore-Roaf-Webster  (1912), 
S0rensen  (1917).  See  also  "Blood,"  "Comparative  and  General 
Physiology." 

Dry-Cells. 

Reference.    Haller-Ritchie  (1920). 

Electroplating.  The  potential  at  which  hydrogen  is  de- 
posited freely  upon  an  electrode  is  a  function  of  the  hydrogen  ion 
concentration  of  the  solution.  Therefore  pH  is  important  in 
controlling  gassy  deposits.  In  addition  it  is  found  that  buffer 
solutions,  maintaining  the  pH  within  definite  limits,  aid  in  the 
production  of  desirable  qualities  in  nickel  deposits. 

References.  Bennett-Rose-Tinkler  (1915),  Blum  (1920,  1921), 
Kiister  (1900),    Thompson  (1922). 

Electrophoresis  (Cataphoresis)  and  Electro-Osmosis. 
An  electrically  charged  body  placed  between  an  anode  and  a 
cathode  will  tend  to  move  toward  the  pole  having  a  charge  opposite 
in  sign  to  the  charge  on  the  body.  If  the  body  is  a  simple  ion, 
the  movement  is  called  ionic  migration.     If  the  body  is  a  particle 


APPLICATIONS  331 

suspended  in  a  medium  such  as  water,  the  movement  is  called 
electrophoresis.  More  generally  it  is  known  as  cataphoresis. 
The  distinction  between  ionic  migration  and  electrophoresis  is 
not  always  clear  in  the  case  of  material  in  the  colloidal  state. 

We  shall  not  discuss  the  various  theories  advanced  to  account 
for  the  experimental  facts  but  shall  treat  briefly  only  that  point 
of  view  which  it  will  be  profitable  to  investigate  further  with 
the  aid  of  methods  for  determining  pH. 

Since  acidic  or  basic  ionization  may  determine  the  sign  of  the 
charge  upon  a  body  of  amphoteric  nature  the  sign  may  be  a  func- 
tion of  the  pH  of  the  medium  (aqueous).  The  direction  of  elec- 
trophoresis is  then  a  function  of  pH.  At  the  isoelectric  point 
electrophoresis  is  a  minimum.  The  position  of  this  minimum  on 
the  pH  scale  is  a  function  of  the  acidic  and  basic  dissociation  con- 
stants and  the  zone  of  the  minimum  may  be  narrow  or  broad 
according  to  the  relative  magnitudes  of  the  constants.  See 
Chapter  1.  The  method  of  electrophoresis  is  useful  in  determin- 
ing isoelectric  points. 

There  can  be  no  movement  such  as  that  noted  above  without 
a  reciprocal  interaction  between  suspended  or  dissolved  material 
and  the  dispersing  medium.  If  then  the  charged  particles  are 
fixed  in  position,  as  in  the  form  of  a  porous  diaphragm,  are  placed 
in  water  and  the  whole  subjected  to  a  potential  gradient,  the 
water  will  tend  to  move  (electro-osmosis).  The  same  relative 
relations  indicated  above  then  hold.  If  the  diaphragm  is  of  an 
amphoteric  nature  the  direction  of  water  flow  will  depend  upon 
the  acidic  and  basic  properties  of  the  diaphragm  and  upon  the 
pH  of  the  aqueous  phase. 

In  either  one  of  the  two  cases  (particles  fixed  or  free  to  move) 
the  same  end  result  will  be  obtained  if  the  particles  adsorb  hydro- 
gen and  hydroxyl  ions  according  to  such  adsorption  isotherma 
that  equality  of  adsorption  and  consequently  equality  of  elec- 
trical charge  is  attained  at  a  definite  pH  value.  On  either  side  of 
this  pH  value  the  excess  adsorption  of  one  or  the  other  ion  will 
depend  upon  their  concentrations  which  are  a  function  of  pH 
by  reason  of  the  relation  [H+]  [OH-]  =  Kw.  The  position  of  this 
"isoelectric"  point  is  a  function  of  the  properties  of  the  material 
and  may  lie  anywhere  along  the  pH  scale  (according  to  the  nature 
of  the  material)  with  a  narrow  or  broad  isoelectric  zone. 


332  THE    DETERMINATION    OF   HYDROGEN    IONS 

The  converse  to  the  above  propositions  is  that  nitration  pro- 
duces a  potential  difference  across  the  filter  which  is  a  function 
of  the  acidic  and  basic  nature  of  the  filter  and  of  the  pH  of  the 
solution  filtered. 

Obviously  the  above  sketch  covers  restricted  conditions. 

References.  Barratt-Harris  (1912),  Briggs  (1918),  Freundlich 
(1921)  Gyemant  (1921),  Michaelis  (1914,  1922),  Perrin  (1904- 
1905),  Porter  (1921),  Putter  (1921),  Steigmann  (1920),  Szent- 
Gyorgyi  (1920,  1921),  Svedberg  (1916),  Svedberg-Anderson 
(1919).     See  also  "Isoelectric  Point." 

Enzymes.  The  activity  of  enzymes  as  influenced  by  the  hy- 
drogen ion  concentration  of  the  solution  has  occupied  the  atten- 
tion of  many  investigators  since  the  publication  of  S0rensen's 
paper  (1909).  The  analogy  between  the  activity  curves  of  several 
enzymes  and  the  curves  relating  the  "dissociation  residues"  of 
amphoteric  electrolytes  to  pH  suggested  to  Michaelis  the  ampho- 
teric nature  of  enzymes  (cf.  Loeb  1909).  Northrop  has  shown 
important  relations  of  activity  to  the  acid-base  nature  of  the 
substrate.  Holderer's  observations  on  the  extraction  of  enzymes 
from  cells  with  solvents  of  different  reaction  are  most  suggestive. 
The  necessity  of  controlling  the  pH  of  enzyme  solutions  for  assays 
as  well  as  in  the  study  of  the  effect  of  salts  and  in  experiments 
having  to  do  with  the  formulation  of  the  laws  of  enzyme  activity 
(Van  Slyke  and  Cullen)  is  now  generally  recognized.  Barendrecht 
in  the  development  of  his  radiation  theory  notes  the  special  im- 
portance of  the  hydrogen  ions. 

The  following  is  a  rough  classification  of  studies  on  specific 
enzymes. 

Amygdalase.     Bertrand-Compton  (1921). 

Amylase.  Ambard  (1921),  Biederman-Rueha  (1921),  Euler- 
Svanberg  (1921),  Falk-McGuire-Blount  (1919),  Maestrini  (1921), 
Groll  (1920),  McGuire-Falk  (1920),  Sherman  (1919),  Sherman- 
Thomas-Baldwin  (1919),  Sherman-Schlessinger  (1915),  Sherman- 
Thomas  (1915),  Sherman-Walker  (1917),  Sjoberg  (1920), 
Takamine-Oshima  (1920). 

Bacterial  enzymes.  Abderhalden-Fodor  (1921),  Avery-Cullen 
(1920),  Barthel-Sandberg  (1920),  Blanc-Pozerski  (1920),  Clark 
(1920),  Dernby  (1917),  Dernby-Blanc  (1921),  Groer  (1912),  Itano 
(1916),  Kanitz  (1903),  Lord  (1919),  Meyer  (1911),  Nye  (1922), 
Waksman(1918),  West-Stevens  (1921). 


APPLICATIONS  333 

Carboxylase.    Neuberg  (1915). 

Catalase.  Bodansky  (1919),  Burge  (1920),  Euler-Blix  (1919), 
Falk-McGuire-Blount  (1919),  Harvey  (1920),  Michaelis-Pechstein 
(1913,  1914),  Morgulis  (1921),  Phragmen  (1919),  Senter  (1905), 
S0rensen  (1909),  Sjoberg  (1920),  Waentig-Steche  (1911). 

Gellase.    Bertrand-Holderer  (1910). 

"Diastases"  (Important  historical  references)  Fernbach  (1906), 
Fernbach-Hubert  (1900). 

Filtration  of.    Holderer. 

Glycogenase.    Norris  (1913). 

Coferments.    Biederman  (1921),  Tholin  (1921). 

Emulsin.  Bayliss  (1912),  Nordefeldt  (1921),  Vulquin  (1910). 
Willstatter-Csanyi  (1921). 

Erepsin.     Euler  (1907),  Dernby  (1916),  Rona-Arnheim  (1913). 

Esterases  (lipase).  Avery-Cullen  (1920),  Baur  (1909),  David- 
sohn  (1912-1913),  Falk,  I.  (1918),  Falk,  K.  (1916),  Groll  (1920), 
Haley-Lyman  (1921),  Hulton-Frankel  (1917),  Kastle  (1902), 
Rona  (1911),  Rona-Bien  (1914),  Rona-Reinicke  (1921),  Rona- 
Michaelis(1911). 

Invertase.  Bertrand-Rosenblatt-Rosenblatt  (1912),  Euler 
(1921),  Euler-Laurin  (1919,  1920),  Euler-Svanberg  (1918-21), 
Fales-Nelson  (1915),  Falk-McGuire  (1921),  Fodor  (1921),  Griffin- 
Nelson  (1916),  Hudson  (1910),  Hudson-Paine  (1910),  Kanitz 
(1911),  Langefeldt  (1921),  Michaelis  (1921),  Michaelis-Davidsohn 
(1911),  Michaelis-Menten  (1913),  Michaelis-Pechstein  (1914), 
Michaelis-Rothstein  (1920),  Nelson-Griffin  (1916),  Nelson-Hitch- 
cock (1921),  Nelson-Vosburgh  (1917),  Rona-Bach  (1921),  Rona- 
Bloch  (1921),  Sjoberg  (1921),  S0rensen  (1909),  Vosburgh  (1921). 

Lactase.    Davidsohn  (1913). 

Levanase.    Kopeloff-Kopeloff-Welcome  (1920). 

Maltase.  Adler  (1916),  Kopaczewski  (1912,  1914,  1915), 
Michaelis-Rona  (1913,  1914),  Rona-Michaelis  (1913). 

Oxidases,  etc.  Bunzel  (1915),  Bunzell  (1916,  1917),  Ohlsson 
(1921),  Menten  (1919,  1920),  Reed  (1916),  Rose-Kraybill-Rose 
(1920). 

Oxynitrilase.     Krieble-Wieland  (1921). 

Pectase.    Euler-Svanberg  (1919). 

Optimum  temperature.  Compton  (1915,  1921).  Euler-Laurin 
(1920).  •     ' 


334  THE    DETERMINATION    OF   HYDROGEN    IONS 

Papain.    Frankel  (1917).     Chesnut  (1920). 

Peroxidase.     Bouma-Van  Dam  (1918). 

Pepsin.  Christiansen  (1912),  Van  Dam  (1915),  Davidsohn 
(1912),  Funk-Niemann  (1910),  Gies  (1902),  Graber  (1921), 
Groll  (1920),  Gyemant  (1920),  Loeb  (1909),  Michaelis  (1918), 
Michaelis-Mendelsohn  (1914),  Michaelis-Rothstein  (1920),  North- 
rop (1919,  1920,  1921),  Okada  (1916),  Pekelharing-Ringer 
(1911),  Ringer  (1918),  Rohonyi  (1912),  S0rensen  (1909). 

Phosphatase.     Adler  (1915). 

Rennet.  Allemann  (1912),  Van  Dam  (1908,  1909,  1912,  1915), 
Funk-Niemann  (1910),  Madsen-Walbum  (1906),  Michaelis- 
Mendelsohn  (1913),  Michaelis-Rothstein  (1920),  Milroy  (1915), 
Thaysen  (1915). 

Salivary  diastase  (ptyalin).  Cole  (1903),  Hahn-Harpuder 
(1920)  Michaelis-Pechstein  (1914),  Ringer-Trigt  (1912).  See 
amylase. 

Taka-diastase.     Okada  (1916). 

Trypsin.  Auerbach-Pick  (1913),  Hahn-Mickalik  (1921),  Ka- 
nitz  (1902),  Michaelis-Davidsohn  (1911),  Northrop  (1921,  1922), 
Palitzsch-Walbum  (1912).  Ringer  (1921),  Robertson-Schmidt 
(1908). 

Theory  of  action.  Barendrecht  (1920),  Euler  (1920),  Falk 
(1921),  Loeb  (1909),  Michaelis  (1909.  1914),  Michaelis-Davidsohn 
Mad    1911),   Rohonyi    (1911),  Van  Slyke-Cullen  (1914). 

Urease.  Barendrecht  (1920),  Lovgren  (1921),  Onodera  (1915), 
Rona-Gyorgy  (1920),  Rona-Petrov  (1920),  Van  Slyke-Cullen 
(1914),  Van  Slyke-Zacharias  (1914). 

Equilibria.  The  hydrogen  electrode  and  indicators  in  the 
determination  of  affinity  constants,  free  energy,  hydrolysis,  etc. 

References.  Adolf-Pauli  (1921),  Bjerrum  (1907-21), 
Boeseken-Kerstjens  (1916),  Bogue  (1920),  Chow  (1920), 
Denham  (1908),  Eucken  (1907),  Ellis  (1916),  Ferguson' (1916), 
Frary-Nietz  (1915),  Fricke  (1920),  Hardman-Lapworth  (1911), 
Harned  (1915-1922),  Heyrovsky  (1920),  Jahn  (1900,  1901), 
Kanitz  (1921),  Lewis  (1908,  1912,  1913),  Lewis-Brighton-Se- 
bastian (1917),  Lewis-Randall  (1914),  Linhart  (1919),  Loffler- 
Spiro  (1919),  Loomis-Acree  (1911),  Loomis-Essex-Meacham 
(1917),  Lowenherz  (1896),  Margaillan  (1913),  McBain-Coleman 
(1914),  Maclnnes  (1919),  Merrill  (1921),  Nernst  (1889),  Newbery 


APPLICATIONS  335 

(1914),  Noyes-Ellis  (1917),  Noyes-Freed  (1920),  Richards-Dun- 
ham (1922),  Rosenheim-Leyser  (1921),  Tizard  (1910),  Tizard- 
Boeree  (1920),  Tolman-Greathouse  (1912).  See  also  Chapters 
IV,  VI,  XVI. 

Explosives. 

References.    Farmer  (1920),  Angeli-Errani  (1920). 

Feces.    See  "Digestive  System." 

Filtration.  Hydrogen  ion  concentration,  through  its  influ- 
ence upon  the  dispersion  of  certain  colloids  and  upon  the  condi- 
tioning of  filter  material,  may  control  the  filterability  of  a  sub- 
stance. Holderer's  thesis  from  Perrin's  laboratory  presents  in 
admirable  form  many  of  the  theoretical  aspects  of  the  subject.  A 
republication  of  this  rare  thesis  is  desired.  The  subject  is  not  only 
of  considerable  theoretical  interest  but  also  of  great  practical 
importance.  Buffer  control  with  indicator  tests'  may  in  many  in- 
stances facilitate  filtrations  upon  an  industrial  as  well  as  a  labo- 
ratory scale. 

References.  Aubel-Colin  (1915),  Holderer  (1909,  1910,  1911, 
1912),  Homer  (1917),  Loeb  (1919),  Schmidt  (1914),  Strada  (1908), 
Wilson  (1921),  Wilson-Copeland-Heisig  (1921),  Wilson-Heisig 
(1921).     See  also  "Electrophoresis." 

Foods,  pH  of.  The  National  Canners'  Laboratory  has  made 
a  number  of  determinations  of  the  pH  of  canned  foods.  See 
"Canning."  See  also  "Milk,"  "Cheese,"  "Wine,"  "Beer,"  "Vine- 
gar," references  given  by  Clark  and  Lubs  (1917)1  and  the  paper 
by  McClendon  and  Sharp  (1919).  The  influence  of  the  pH  upon 
the  stability  of  a  "vitamine"  has  been  studied  by  La  Mer  (1921), 
and  Campbell,  LaMer  and  Sherman  (1922).  cf.  Harden  and 
Zilva  (1918).  For  sterilization  of  canned  goods  see  "Disinfec- 
tion" under  "Bacteriology"  and  "Canning". 

Glass,  effect  of,  on  reaction  of  solutions. 

References.  Esty-Cathcart  (1921),  Ewe  (1920),  Fabian-Stull 
(1921),    Levy-Cullen    (1920),    Russell-Nichols-Stimmel    (1920). 

Glucose,  decomposition  of,  as  influenced  by  pH. 

References.  Elias-Kolb  (1913),  Euler-Hedelius  (1920),  Hen- 
derson    (1911),     Mathews-McGuigan     (1907),     Michaelis-Rona 

1  Some  of  the  pH  values  given  by  Clark  and  Lubs  for  acidified  or  alka- 
linized  extracts  have  been  misquoted  as  the  pH  values  of  the  original 
material. 


336  THE    DETERMINATION    OF   HYDROGEN   IONS 

(1909-1912),  Nef  (1913),  Rona-Arnheim  (1913),  Rona-Doblin 
(1911),  Rona-Wilenko  (1914).    Also  references  in  Woker. 

Hemolysis  , 

References.  Atkin  (1911,  1914),  Cook-Mix-Culvyhouse  (1921), 
Coulter  (1921),  Fenn,  (1922),  Fuhner-Neubaur  (1907),  Gros 
(1910),  Haffner  (1920),  Hellens  (1913),  Jodlbauer-Haffner  (1920, 
1921),  Jordan  (1903),  Kozawa  (1914),  Krogh  (1909),  Lagrange 
(1914),  Michaelis-Skwirsky  (1909),  Michaelis-Takahashi  (1910), 
Stevens-Koser  (1920),  Teague-Buxton  (1907),  Walbum  (1914, 
1915). 

Hydrolysis.  The  reaction  between  an  acid  and  a  base  is 
reversible. 

HA  +  BOH  ?=±  BA  +  H20 

♦ 

There  are  present  then  both  free  acid  and  free  base  even  when 
the  two  are  mixed  in  equivalent  proportions.  This  last  condition 
can  be  duplicated  by  making  up  the  solution  in  the  first  place 
with  the  pure  salt.  The  above  reaction  then  goes  from  right  to 
left  until  the  equilibrium  state  is  reached  and  the  process  is 
called  hydrolysis,  because  it  may  be  regarded  as  a  splitting 
of  water  molecules. 

Now  the  resulting  acid  and  base  ionize,  the  one  tending  to 
increase  the  hydrogen  ion  concentration,  the  other  tending  to 
increase  the  hydroxyl  ion  concentration.  If  the  acid  is  more 
highly  dissociated  than  the  base  the  solution  will  contain  more 
hydrogen  ions  than  hydroxyl  ions;  and  if  the  base  is  more  highly 
dissociated  than  the  acid  the  solution  will  contain  more  hydroxyl 
than  hydrogen  ions.  Since  the  magnitude  of  a  dissociation  con- 
stant is  a  measure  of  dissociation  tendency  the  reaction  of  a  salt 
solution  will  depend  upon  the  relative  magnitudes  of  the  Ka 
and  Kb  constants  of  the  component  acid  and  base. 

In  a  solution  of  the  salt,  BA,  we  have  present  BA,  B+,  A-, 
HA,  BOH,  H+  and  OH.~ 

By  the  rule  of  electrical  neutrality  [A~]  +  [OH"]  =  [B+]  + 
[H+].  Since  total  acid  =  total  base,  [HA]  +  [A~]  +  [BA]  =  [B+] 
-f  [BOH]  +  [BA].  Introducing  the  acid  and  the  base  equilib- 
rium equations  and  the  relation  [H+]  [OH-]  =  Kw  and  combining 
these  equations  we  have 


mn  =  VK- ' 


Kb  (K.  +  [Ai) 


APPLICATIONS  337 

If  now  Kb  and  Ka  are  small  in  relation  to  [B+]  and  [A-],  and 
if  the  solution  is  sufficiently  dilute  so  that  [B+]  and  [A-]  each 
approximate  the  salt  concentration  [S],  then  approximately 


[h+]  =  VKwi^ 


Cf.  formula  for  isoelectric  point  of  ampholyte.    When  Ka  =  Kb, 
[H+]  =  10-7,  pH  =  7. 

If  we  are  dealing  with  a  salt,  the  acid  component  of  which 
is  very  "strong"  we  may  regard  the  acid  set  free  by  the  hydroly- 
sis of  the  salt  as  completely  dissociated.  [HA]  in  the  above  equa- 
tions is  placed  equal  to  zero  and  we  then  derive 

[H+]=  ^(Kh  +  [B+]) 
"  Kb 

If  now  Kb  is  small  in  relation  to  [B+]  and  if  [B+]  approxi- 
mates [S] 

[H+]  approximates  \— -  [S] 
™  Kb 

Conversely  when  the  base  is  very  strong  and  when  the  same 
assumptions  made  above  are  maintained 


[H+]  approximates  W 


KaKv 


[S] 


References.  See  treatment  by  Bjerrum  (1914),  example  by 
Denham  (1908),  and  numerous  references  under  "Equilibria." 

Indicator  Constants.  See  Prideaux  and  Chapters  IV  and 
VIII. 

,  References.  Clark-Lubs  (1917),  Gillespie  (1920),  Paulus-Hut- 
chinson-Jones  (1915),  Kolthoff  (1918-1922),  Michaelis  (1920), 
Michaelis-Gyemant  (1920),  Michaelis-Kriiger  (1921),  Rosenstein 
(1912),  Schaeffer-Paulus-Jones  (1915),  Salm  (1904),  Tizard  (1910). 

Indicators,  natural. 

References.  Bribaker  (1914),  Crozier  (1916,  1918),  Haas  (1916), 
Pozzi-Escot  (1913),  Sacher  (1910),  Scheitz  (1910),  Stephanides 
(1916),  Trillat  (1916),  Walbum  (1913),  Watson  (1913).  See  also 
Perkin  and  Everest. 


338  THE    DETERMINATION    OF   HYDROGEN   IONS 

Industrial  Processes.  See  every  subject  in  this  chapter. 
Also  the  following  special  references. 

References.  Brewster-Raines  (1921),  Clark-Zoller-Dahlberg- 
Weimar  (1920),  Keeler  (1922),  Lubs  (1920),  Searle  (1920),  Wil- 
son-Copeland-Heisig  (1921),  Wilson-Heisig  (1921),  Zoller/1921), 
and  references  on  "Water  Works"  and  "Leather." 

Isoelectric  Points.    See  Chapter  I. 

References.  Brossa  (1915),  Cohn  (1920-1922),  Cohn-Gross- 
Johnson  (1920),  Eckweiler-Noyes-Falk  (1920),  Fodor  (1920), 
Loeb  (1918-1922),  Michaelis  (1911-1920),  Michaelis-Bien  (1914), 
Michaelis-Davidsohn  (1910-1913),  Michaelis-Grineff  (1912), 
Michaelis-Mostynski  (1910),  Michaelis-Pechstein  (1912),  Michae- 
lis-Rona  (1919),  Michaelis-Takahashi  (1910),  Mills  (1921), 
Rona-Michaelis  (1910),  S0rensen  (1912,  1917),  Stuber-Funck 
(1921),  Szent  Gyorgyi  (1921),  Thomas-Kelley  (1922). 

Leather  and  Tanning. 

References.  Atkin  (1922),  Atkin-Atkin  (1920),  Atkin-Thomp- 
son  (1920),  Balderston  (1913),  Procter  (1921),  Procter-Wilson 
(1916),  Povarnin  (1915),  Sand-Law  (1911),  Thomas-Baldwin 
(1919),  Thomas-Foster  (1921),  Thomas-Kelly  (1921,  1922), 
Wilson  (1917,  1921),  Wilson-Daub  (1921),  Wilson-Kern  (1921), 
Wood-Sand-Law  (1911).     See  also  "Proteins." 

Milk. 

References.  Allemann  (1912),  Aron  (1914),  Baker-Breed  (1920)/ 
Baker-Van  Slyke  (1919),  Chapman  (1908),  Clark  (1915),  Clark- 
Cohen  (1922),  Cooledge-Wyant  (1920),  van  Dam  (1908,  1918), 
Davidsohn  (1912,  1913),  Foa  (1905,  1906),  Hastings-Davenport 
(1920),  Jones  (1921),  Kramer-Green  (1921),  Laqueur-Sackur 
(1903),  Milroy  (1915),  Palmer-Dahle  (1922)  Rogers-Deysher- 
Evans  (1921),  Rona-Michaelis  (1909),  Schultz-Chandler  (1921), 
Schultz-Marx-Beaver  (1921),  Sommer-Hart  (1919,  1920),  Stut- 
terheinn,  Szili  (1917),  Taylor  (1913),  Terry  (1919),  Till- 
mans-Obermeier  (1920),  Van  Slyke-Baker  (1918,  1919).  See  also 
"Cheese"  and  "Protein." 

Neuro-physiology. 

References.  Adrian  (1920),  Bottazzi-Craifaleanu  (1916),  Chid 
(19,07),  Garry  (1920),  Grant  (1920),  Mansfield-Szent  Gyorgyi 
(1920),  Mayer  (1916),  Moore  (1919),  Neugarten  (1919),  Zotter- 
man  (1921).  See  also  "Blood,"  (the  respiration  phase)  and 
"Comparative  and  General  Physiology." 


APPLICATIONS  339 

Permeability  of  cells. 

References.  Bethe  (1922),  Clowes-Smith  (1922),  Collander 
(1920),  Donnan  (1911),  Haas  (1916),  Harvey  (1911,  1913),  Haynes 
(1921),  Holderer  (1911),  Jacob j  (1920),  Lillie  (1909),  Moore-Roaf- 
Webster  (1912),  Oden  (1916),  Reemelin-Isaacs  (1916),  Snapper 
(1913),  Stiles-Jorgensen   (1915),   compare  Filtration. 

Phagocytosis. 

References.  A.  Evans  (1921, 1922),  Hamberger-Heckma  (1908) , 
Koltzoff  (1914),  Radsma  (1920),  Sawtchenko-Aristovsky  (1912), 
Schwyzer  (1914). 

Pharmacology,  etc.  pH  in  relation  to  properties,  activity, 
deterioration,  and  assay  or  detection  of  drugs. 

References.  Adams  (1917),  Crane  (1921),  Evers(1921),v.Groer- 
Matula  (1920),  Hanzlik  (1920,  1921),  Kolthoff,  (1920,  1922), 
Leech  (1922),  Levy-Cullen  (1920),  Macht-Shohl  (1920),  Meier- 
Kronig  (1921),  Mellon-Slagle-Acree  (1922),  Menten  (1920), 
Moore  (1920),  Rippel  (1920),  Rona-Bach  (1920),  Shohl-Deming 
(1921),  Snyder-Campbell  (1920),  Sollmann  (1917),  Tsakalotos- 
Horsch  (i914),  Williams-Swett  (1922),  Zoccola  (1918). 

Phyto-pathology  and  Physiology. 

References.  Atkins  (1922),  Chambers  (1921),  Clevenger  (1919), 
Crozier  (1919),  Harvey  (1920),  Hixon  (1920),  Lapicque  (1921), 
MacDougal  (1921),  Martin  (1921),  Schmitz  (1919),  Schmitz- 
Zeller  (1919),  Webb  (1919),  Wherry  (1918-22),  Wolf-Foster 
(1921),   Wolf-Shunk  (1921),  Zeller-Schmitz  (1919). 

See  "Plant  Distribution,"  "Comparative  and  General  Physi- 
ology," "Soil." 

Plant  Distribution.  Wherry,  working  with  a  simple  field 
kit,  has  carried  indicators  into  the  field  and  has  correlated  the 
habitats  of  several  plant  species  with  the  pH  of  their  soils. 

Investigations  by  O.  Arrhenius  in  Sweden,  by  Olsen  in  Denmark 
and  by  Atkins  in  England  and  India  have  confirmed  Wherry's 
observation  that  the  pH  of  the  soil  is  of  great  significance. 

Such  information  has  contributed  toward  methods  of  cultivat- 
ing the  blueberry  and  wild-flowers  hitherto  unknown  or  un- 
common in  garden  and  greenhouse. 

References.  Arrhenius  (1920,  1922),  Atkins  (1921,  1922), 
bomber  (1921),  Emerson  (1921),  Fisher  (1921),  Gail  (1919), 
)lsen  (1921),  Wherry  (1920-1922).  See  also  "Phytopathology 
tnd  Physiology,"  "  Soils,"  "Water,"  and  especially  " Bacteriology." 


34:0         THE  DETERMINATION  OF  HYDROGEN  IONS 

Proteins,  by  reason  of  their  chemical  structure,  are  amphoteric. 
As  such  they  are  subject  to  the  pH  of  aqueous  dispersing  media 
as  are  the  simple  ampholytes.  Though  complete  equilibrium 
equations  are  difficult  to  formulate  we  should  expect  the  occur- 
rence of  pH  points  and  zones  comparable  to  the  isoelectric  points 
and  zones  of  simple  ampholytes.  Experimentally  these  have 
been  found.  These  are  also  points  of  optima,  or  minima,  for 
various  properties  of  protein  solutions  (e.g.  minimal  electrophore- 
sis, viscosity  and  osmosis).  If  the  solubility  of  the  protein  itself 
is  less  than  that  of  its  acid  or  basic  salts,  the  protein  can  be  pre- 
cipitated at  or  near  the  isoelectric  point  (e.g.  analysis  and  com- 
mercial preparation  of  casein).  Closely  related  is  the  adjustment 
of  pH  favoring  separation  of  crystals.  Proteins  are  unable  to 
penetrate  many  membranes  but  are  able  to  enter  into  an  acid- 
base  equilibrium  and  thus  exhibit  many  interesting  relations  in 
Donnan  equilibria  (S0rensen,  Loeb). 

The  outstanding  difficulty  in  treating  proteins  as  electrolytes 
is  the  establishment  of  exact  quantities  for  concentrations  or 
activities  which  must  necessarily  be  used  in  formulating  equilib- 
rium equations.  The  mathematical  treatment  by  Michaelis 
and  by  S0rensen,  and  especially  the  painstaking  experimental 
investigations  to  which  S0rensen  and  his  coworkers  have  devoted 
several  years  have  advanced  the  subject  beyond  dependence  on 
mere  analogy  to  the  conduct  of  simple  ampholytes. 

References.  Adolf -Spiegel  (1920),  Agostino-Quagliariello  (1912), 
Atkin  (1920),  Bogue  (1921),  Bovie  (1920),  Bugarszky-Liebermann 
(1898),  Burrows-Cohn  (1918),  Chiari  (1911),  Chick  (1913), 
Chick-Martin  (1910-13),  Clark-Zoller-Dahlberg-Weimar  (1920), 
Cohn  (1920-22), Cohn-Gross-Johnson  (1920),Davis-Oakes-Browne 
(1921),  Ferguson-France  (1921),  Field  (1921),  Fodor  (1920-21), 
Haas  (1918),  Handovsky  (1910),  Hardy  (1899,  1905),  Henderson- 
Cohn-Cathcart-Wachman-Fenn  (1919),  Henderson-Palmer-Neu- 
burgh  (1914),  Hill  (1921),  Hitchcock  (1922),  Laqueur-Sackur, 
(1903),  Lloyd  (1920,  1922),  Loeb  (1918-22),  Manabe-Matula 
(1913),  Michaelis  (1909),  Michaelis-Airila  (1921),  Michaelis- 
Mostynski  (1910),  Michaelis-Rona  (1910,  1919),  Michaelis- 
Szent  Gyorgyi  (1920),  Mills  (1921),  Okuda-Zoller  (1921),  Oryng- 
Pauli  (1915),  Palmer-Atchley-Loeb  (1921,  1922),  Patten-John- 
son   (1919),    Patten-Kelems    (1920),    Pauli    (1903-1922),    Pauli- 


APPLICATIONS  341 

Handovsky  (1908-10),  Pauli-Matula  (1919),  Pauli-Samec  (1909- 
14),  Pauli-Wagner  (1910),  Pechstein  (1913),  Procter-Wilson 
(1916),  Quagliariello  (1912),  Resch  (1917),  Robertson  (1907- 
1918),  Rohonyi  (1912),  Ryd  (1917,  1918),  Sharp-Gortner  (1922), 
Schmidt  (1916),  Schorr  (1911),  Sollmann  (1917),  S0rensen  (1917- 
1921),  S0rensen  &  coworkers  (1917),  S0rensen-Jiirgensen  (1911), 
Spiro  (1904,  1913),  Starke  (1900),  Szent-Gyorgyi  (1920,  1921), 
Thomas  (1921),  Wagner  (1921),  Wintgen-Kriiger  (1921),  Wint- 
gen-Vogel  (1922),  Ylppo  (1913),  Zoller  (1921).  See  also  "Iso- 
electric Point." 

Salt-Action,  theory  and  effects  in  relation  to  pH.  See  Chap- 
ters I,  II,  and  VII. 

References.  Abegg-Bose  (1899),  Arrhenius  (1888,  1889),  Aker- 
lof  (1921),  Brightman-Meachem-Acree  (1920),  Chick-Martin 
(1912,  1913),  Falk  (1918,  1920),  Gillespie- Wise  (1918),  Harned 
(1915),  Haynes  (1921),  Hofmeister  (1891),  Holm-Sherman  (1921- 
1922),  Kolthoff  (1916-22),  Lloyd  (1916),  Loeb  (1906-1922), 
McBain-Coleman  (1914),  McClendon-Mitchell  (1912),  Michaelis 
(1914,  1920),  Michaelis-Rona  (1909),  Michaelis-Szent  Gyorgyi 
(1920),  Michaelis-Timenez  Dias  (1921),  Northrop  (1920),  Poma 
(1914),  Poma-Patson  (1914),  Prideaux  (1919),  Rose-Kraybill-Rose 
(1920),  Rosenstein  (1912),  Ryd  (1917),  Shearer  (1920),  Sherman- 
Thomas  (1915),  S0rensen-Palitzsch  (1913),  S0rensen-S0rensen- 
Linderstr0m  Lang  (1921),  Spiro  (1921),  Szent-Gyorgyi  (1920), 
Szyszkowski  (1907),  Thomas  Baldwin  (1919),  Wells  (1920),  See 
especially  references  in  Chapter  II  on  "Activity." 

Serology.  See  also  Acid  Agglutination  of  Bacteria,  Hemolysis, 
Bacteriology,  Proteins,  Colloids. 

References.  Amako  (1911),  Atzler  (1914),  Brooks  (1920), 
Buchanan  (1919),  Coulter  (1921),  Enlows  (1922),  Evans  (1921, 
22),  Field-Teague  (1907),  Hirsch-Peters  (1922),  Homer  (1917, 
1918,  1919),  Landensteiner  (1913),  Landensteiner-Prasek  (1913), 
Langenstrass  (1919),  Lindenschatt  (1913),  Leschly  (1916),  Ma- 
son (1922),  Michaelis-Davidsohn  (1912),  Neukirch  (1920),  No- 
guchi  (1907),  Ruppel  (1920),  Tulloch  (1914,  1918). 

Sewage. 

References.  Clark-Cohen  (1922),  Wilson-Copeland-Heisig 
(1921),  Wilson-Heisig  (1921). 


342  the  determination  of  hydrogen  ions 

Soap  Solutions. 

References.  Beedle-Bolam  (1921),  McBain  (1920),  McBain- 
Bolam  (1918),  McBain-Martin  (1918),   McBain-Salmon  (1920). 

Soil  Acidity  has  been  confused  by  the  complexities  of  titri- 
metric  procedures,  has  been  neglected,  or  has  been  considered  to  be 
an  unreality  by  one  or  another  school.  Gillespie  (1916)  obtained 
good  agreement  between  pH  values  of  soil  extracts  determined 
by  means  of  the  hydrogen  electrode  and  again  by  means  of  indi- 
cators. The  practical  significance  of  this  is  now  revealed  by 
studies  which  show  characteristic  pH  values  for  well-defined  types 
of  soil,  which  show  correlations  between  the  pH  of  soil  extracts 
and  the  growth  of  beneficial  or  harmful  microorganisms,  and 
which  show  correlations  between  the  natural  distribution  of 
plants  and  the  pH  of  the  soils  in  which  they  are  found. 

References.  Arrhenius  (1921,  1922),  Atkins  (1922),  Bjerrum- 
Gjaldbaek  (1919),  Blair-Prince  (1920),  Carr  (1921),  Comber 
(1920),  Conner  (1921),  Crouther  (1920),  Demolon  (1920),  Dug- 
gar  (1920),  Erdman  (1921),  Fisher  (1914,  1921),  Gainey  (1918, 
1922),  Gillespie  (1916-1918),  Gillespie-Hurst  (1918),  Hibbard 
(1921),  Hoagland  (1917-1918),  Hoagland-Christie  (1918),  Hoag- 
land-Sharp  (1918),  Hudig-Strum  (1919),  Joffe  (1920),  Jones- 
Shive  (1920),  Kappen  (1916),  Kappen-Zapfe  (1917),  Kelley- 
Cummins  (1921),.  Knight  (1920),  Kobayashi  (1920),  Lipman- 
Joffe  (1920),  Lipman-Waksman-Joffe  (1921),  Loew  (1903), 
xMcCall-Haag  (1920,  1921),  MacDougal  (1920),  Martin  (1920, 
1921),  Meier-Halstead  (1921),  Morse  (1918,  1920),  Oden  (1916- 
21),  Olsen  (1921),  Plummer  (1918),  Rice-Osugi  (1918),  Robinson 
(1921),  Robinson-Bullis  (1921),  Saidel  (1913),  Salter-Mcllvaine 
(1920),  Schollenberger  (1921),  Sharp-Hoagland  (1916,  1919), 
Stephenson  (1919,  1921),  Stocklasa  (1922)  Swanson-Latshaw- 
Tague  (1921),  Tijmstra  (1917),  Truog  (1918),  Truog-Meacham 
(1919),  Waksman  (1922),  Weis  (1919),  Wherry  (1916-1922). 
See  also  "Plant  Distribution." 

Solubility.  The  true  solubility  of  a  compound  may  be 
regarded  as  independent  of  the  hydrogen  ion  concentration  of  a 
solution;  but  if  the  compound  is  an  acid,  base,  ampholyte  or  salt 
some  of  the  material  present  in  solution  is  ionized  and  this  portion 
is  governed  by  the  ionic  equilibrium  of  which  the  hydrogen  ion 
concentration  is  a  part.     Therefore  the  total  solubility  which  is 


APPLICATIONS  343 

generally  of  more  importance  than  the  true,  partial  solubility 
is  a  function  of  pH. 

[H+]  [A-] 
Consider  the  equilibrium  — =77: —   =    Ka  and   assume   that 

LH-AJ 

the  solubility  of  the  acid  HA  itself  is  low  so  that  we  shall  not 
encounter  the  difficulties  inherent  in  the  treatment  of  concen- 
trated solutions.  If  the  acid  is  present  in  the  solid  phase  [HA] 
is  maintained  constant  and  is  the  partial  solubility,  Sp.  On 
combining  the  constants  in  the  above  equation  we  have  [H+] 
[A-]  =  Ks  where  Ks  is  the  solubility  product.  The  total  solu- 
bility, St  is  then  equal  to  the  true  partial  solubility,  Sp,  plus  [A-]  or 

*•_«  ,  j^    q  _*  nH+] ± Kal 

»t  —  &p  -r  rjj+i'  or  °t  —  &p  ru+i 

If  there  is  present  no  salt  of  the  acid  to  furnish  [A-] 

[Hi2  =  K8 
or 

pH  =  -  }  log  K8 

For  the  case  of  calcium  carbonate,  the  [C03  ]  from  which  is 
controlled  by  [H+],  see  "Carbonate  Equilibria." 

References.  See  any  text  on  physical  chemistry  and  "Carbon- 
ate Equilibria,"   "Protein,"    "Equilibria,"   etc. 

Staining. 

References.  Agulhon-Leobardy  (1921),  Bethe  (1922),  Jodl- 
bauer-Haffner  (1921),  MacArthur  (1921),  Michaelis  (1920), 
Ponselle  (1919),  Rohde  (1920). 

Surface  Tension. 

References.  Adam  (1921),  Bottazzi-Agostino,  Ellis  (1911), 
Haber-Klemensiewicz  (1909),  Hartridge-Peters  (1920),  Micha- 
elis (1909),  Schwyzer  (1914),  Traube  (1920),  Williams  (1920), 
Willows-Hatschek  (1919),   Windish-Dietrich  (1919-1922). 

Sweat. 

References.     Clark-Lubs,  (1917),  Talbert  (1919).       • 

Tautomerism  other  than  of  indicators. 

References.  Biddle-Watson  (1917),  Fraenkel  (1907)  Mur- 
chauser  (1920),  Nelson-Beegle  (1919). 

Tissue  Culture. 

References.    Felton  (1921),  Fischer  (1921),  Lewis-Felton  (1921). 


344  THE  DETERMINATION  OF  HYDROGEN  IONS 

Urine  and  Kidney  Functions.  The  excretion  of  acids  and 
bases  in  the  urine  is  one  of  the  mechanisms  by  which  the  hydrogen 
ion  concentration  of  the  blood  is  preserved  constant.  For  this 
reason  the  determination  of  the  acid-base  equilibria  in  the  urine 
in  their  relation  to  the  potential  acid-base  intake  in  the  food  and 
the  degree  of  oxidation  of  food  material  is  of  importance  in 
fundamental  physiological  researches  and  in  clinical  studies. 
Besides  references  to  be  found  under  "Blood"  the  following  are 
some  of  the  more  special  references  on  urine.2 

References.    Auerbach-Friedenthal  (1903),  Biehler  (1920),  Biltz- 
Hermann    (1921),    Blatherwick    (1914),  Bugarszky  (1897),  Carr 
(1921),     Collip-Backus     (1920),     Cushny    (book    1917),    Fiske 
(1920,  1921),  Fitz-Van  Slyke  (1917),  Foa  (1905),  Gamble  (1922), 
Guillaumin  (1920),  Hanzlik  (1920),  Haskins  (1919),  Hasselbalch 
(1916),  Henderson  (1910,  1911,  1914),  Henderson-Palmer  (1913) 
Henderson-Spiro  (1908),  Hober  (1902),  Hober-Jankowsky  (1903) 
Hollo     (1921)  a    Howe-Hawk    (1914),    Macleod-Knapp    (1918) 
Marshall    (1922),    Nagayama    (1920),    Nelson-Williams    (1916) 
Newburgh-Palmer-Henderson  (1913),  Palmer-Henderson  (1915) 
Palmer-Salvesen-Jackson  (1920),  Quagliariello-d'Agostino  (1912) 
Reemelin-Issacs   (1916),   Rhorer   (1901),    Ringer    (1909,    1910) 
Rohde   (1920),    Schemensky    (1920),    Schloss-Harrington  (1919) 
Shohl  (1920),  Skramlik  (1911),  Stillman-Van  Slyke  (1917),  Tal- 
bert  (1920),  Van  Slyke-Palmer  (1919,  1920). 

Vinegar. 

Reference.  Clark-Lubs  (1917),  Brode-Lange  (1909),  Kling- 
Lassieur-Lassieur  (1922). 

Water  (sea  and  fresh).  The  carbonate  equilibrium  maintains 
sea  water  at  a  very  constant  pH  which  has  doubtless  varied  with 
the  C02  tension  of  the  atmosphere  in  geological  ages  and  which 
varies  somewhat  with  the  temperature,  and  locally  with  accretions 
from  rivers  and  springs  and  contact  with  geologic  deposits.  The 
wider  aspects  of  the  carbonate  equilibria  involved  have  been 
described  in  Henderson's  Fitness  of  the  Environment.  The  chart- 
ing of  the  pH  values  for  different  regions  of  the  seas  has  been 
of  aid  in  oceanographic  surveys  and  in  some  instances  has  been 
of  value  in  the  study  of  plant  and  animal  distribution.  (See 
"Plant  Distribution"  and  "Comparative  Physiology.") 

*  See  Clark  and  Lubs  (1917)  for  some  examples 'of  the  application  of  the 
sulfon  phthalein  indicators  to  the  determination  of  the  pH  of  urines. 


APPLICATION'S  345 

Fresh  waters  are  influenced  chiefly  by  the  deposits  with  which 
they  come  in  contact.  pH  determinations  in  the  field  are  of  aid  to 
the  geologist  in  demarking  waters  of  limestone  origin  (Wherry 
private  communication) . 

In  the  clarification  of  water  by  "alum"  or  "iron"  coagulation 
the  pH  of  the  final  mix  determines  the  percentage  coagulant  thrown 
out,  the  time  required  for  floe  formation  and  the  efficiency  of 
color-  and  turbidity-removal.  There  is  also  a  probable  relation 
to  the  efficiency  of  the  filtration  process  itself. 

The  hydrogen  ion  enters  into  every  equilibrium  of  importance 
to  water  softening  and  to  corrosion. 

References.  Auerbach  (1904),  Baylis  (1922),  Buswell  (1922), 
Corti-Alvarez  (1918),  Crozier  (1920),  Gaarder  (1916-1917), 
Greenfield-Baker  (1920),  Haas  (1916),  Henderson  (1913),  Hen- 
derson-Cohn  (1916),  Heyman  (1920),  Kolthoff  (1921),  Loeb 
(1904),  McClendon  (1916,  1917),  Mayer  (1919),  Massink  (1920), 
Massink-Heyman  (1921),  Michaelis  (1914,  1921),  Palitzsch 
(1911,  1915,  1916),  Powers  (1921,  1922),  Prideaux  (1919),  Ringer 
(1908),  Ruppin  (1909),  Saunders  (1921),  Shelf ord  (1919),  Smith 
(1919),  Snook  (1915),  S0rensen-Palitzsch  (1910-13),  Stephanides 
(1916),  Tillmans  (1919,  1921),  Trillat  (1916),  Wagner-Enslow 
(1922),  Walker-Kay  (1912),  Wells  (1921),  Wolman-Hannan  (1921). 

Water,  pure.     Ionization  of. 

References.  Kohlrausch-Heydweiller  (1894),  Lewis,  Brighton 
and  Sebastian  (1917),  Nernst  (1894),  Ostwald  (1893),  Wijs  (1893). 

Wine  Acidity.  Besides  influencing  the  fermentations,  the  pH 
of  wine  has  been  found  to  correlate  in  a  general  way  with  the  acid 
taste. 

References.  Casale  (1919),  Dutoit-Dubroux  (1910),  Paul 
(1914,  1915,  1916),  Quartaroli  (1912). 


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V 


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\f 


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404 


THE    DETERMINATION    OF   HYDROGEN    IONS 


V 


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